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					Table of Index

EXECUTIVE SUMMARY .............................................................................................................................. 7
INTRODUCTION TO DERIVATIVES ......................................................................................................... 8
DERIVATIVES DEFINED ............................................................................................................................. 9
FACTORS AFFECTING FINANCIAL DERIVATIVES ...................................................................... 10
TYPES OF DERIVATIVES ..................................................................................................................... 10-12
    1.        FORWARDS ...........................................................................................................................................
    2.        FUTURES...............................................................................................................................................
    3.        OPTIONS ...............................................................................................................................................
    4.        SWAPS ..................................................................................................................................................
    5.        WARRANTS...........................................................................................................................................
    6.        LEAPS ...................................................................................................................................................
    7.        SWAPTIONS...........................................................................................................................................
PARTICIPANTS AND FUNCTIONS ..................................................................................................... 12-13
             PARTICIPANTS ......................................................................................................................................
    1.        HEDGERS ............................................................................................................................................. .
              SPECULATORS ......................................................................................................................................
    3.        ARBITRAGEURS ....................................................................................................................................
             ECONOMIC FUNCTIONS .........................................................................................................................
DEVELOPMENT OF EXCHANGE-TRADED DERIVATIVES .............................................................. 14
EXCHANGE-TRADED VS. OTC DERIVATIVES MARKETS.......................................................... 15-16
             FEATURES OF OTC DERIVATIVES MARKET...........................................................................................
             RISK ASSOCIATED WITH OTC DERIVATIVES MARKET ..........................................................................
INDIAN DERIVATIVES MARKET ....................................................................................................... 17-18
             CHRONOLOGY OF INSTRUMENTS...........................................................................................................
             NEED FOR DERIVATIVES IN INDIA TODAY .............................................................................................
FORWARD CONTRACTS & FUTURES & OPTIONS ....................................................................... 18-21
        INTRODUCTION TO FORWARD CONTRACTS............................................................................................
      Features of forward contracts ...................................................................................................................
      Limitations of forward markets .................................................................................................................
        INTRODUCTION TO FUTURES .................................................................................................................
      Standardized items in a futures contract ...................................................................................................
      Futures Terminology .................................................................................................................................
INTRODUCTION TO OPTIONS ........................................................................................................... 22-23
             HISTORY OF OPTIONS ............................................................................................................................
             OPTION TERMINOLOGY ........................................................................................................................
DISTINCTION BETWEEN FUTURES AND FORWARDS CONTRACTS ........................................... 25
             FUTURES VS FORWARDS ......................................................................................................................
DISTINCTION BETWEEN FUTURES AND OPTIONS .......................................................................... 26
             FUTURES VS OPTIONS ..........................................................................................................................
INDEX DERIVATIVES ................................................................................................................................ 27
             ADVANTAGES OF INDEX DERIVATIVFES ...............................................................................................



                                                                                                                                                                 1
PAYOFF & PRICING OF FUTURES AND OPTIONS ........................................................................ 28-35
              PAYOFF FOR FUTURES ...........................................................................................................................
              PAYOFF FOR BUYER OF FUTURES: LONG FUTURES ................................................................................
              PAYOFF FOR SELLER OF FUTURES: SHORT FUTURES ..............................................................................
              OPTIONS PAYOFFS ................................................................................................................................
              PAYOFF PROFILE OF BUYER OF ASSET: LONG ASSET .............................................................................
              PAYOFF PROFILE FOR SELLER OF ASSET: SHORT ASSET .........................................................................
              PAYOFF PROFILE FOR BUYER OF CALL OPTIONS: LONG CALL ................................................................
              PAYOFF PROFILE FOR WRITER OF CALL OPTIONS: SHORT CALL .............................................................
              PAYOFF PROFILE FOR BUYER OF PUT OPTIONS: LONG PUT ....................................................................
              PAYOFF PROFILE FOR WRITER OF PUT OPTIONS: SHORT PUT..................................................................
PRICING .................................................................................................................................................... 36-45
          PRICING INDEX FUTURES ......................................................................................................................
          PRICING FUTURES CONTRACTS ON COMMODITIES .................................................................................
          PRICING FUTURES CONTRACTS ON EQUITY INDEX .................................................................................
          PRICING INDEX FUTURES GIVEN EXPECTED DIVIDEND AMOUNT ............................................................
          PRICING INDEX FUTURES GIVEN EXPECTED DIVIDEND YIELD ................................................................
          PRICING OPTIONS ..................................................................................................................................
       Introduction to the Black–Scholes formulae .............................................................................................
          PRICING INDEX OPTIONS .......................................................................................................................
SWAPS ....................................................................................................................................................... 45-55
            WHY DID SWAPS EMERGE? ...................................................................................................................
            SWAPS PRICING: ...................................................................................................................................
            SWAP MARKET PARTICIPATION’S .........................................................................................................
            CURRENCY SWAPS IN INDIA .................................................................................................................
            THE PLAYERS .......................................................................................................................................
            CURRENCY SWAPS MEETS THE PLAYER NEEDS......................................................................................
            FACTORS TO BE LOOKED AT WHILE DOING A SWAP ...............................................................................
          1.    The estimated net exposure ............................................................................................................
          2.    Expected interest rates ...................................................................................................................
          3.    Amount of cover to be taken ...........................................................................................................
INTRODUCTION OF FORWARD RATE AGREEMENTS AND INTEREST RATE SWAPS ...... 56-57
             OBJECTIVE ............................................................................................................................................
             DESCRIPTION OF THE PRODUCT.............................................................................................................
          Forward Rate Agreement ..........................................................................................................................
          Interest Rate Swap .....................................................................................................................................
MARKET REPORT- ISSUES OF CONCERN ........................................................................................... 58
BIBLOGRAPHY ............................................................................................................................................ 60




                                                                                                                                                              2
Executive Summary

The main objective or purpose of this document is to provide an insight and to
share the information on one of the biggest domain ruling globally is
“Derivatives”.

Review the development of the derivatives market under the current regulatory
regime with limited capital account convertibility.

The information and the data that has been shared through this document will
have a detail description of the below mentioned areas.

    Introduction to Derivatives
    Derivatives Defined
    Factors affecting Financial Derivates
    Types of derivatives
    Participant & Functions
    Evolution of exchange traded derivatives
    Provide an insight about „Future‟, „Forward‟ and „Option‟ contracts
    Detailing about „SWAPS‟
    Information on pricing




                                                                           3
Introduction to Derivatives
The emergence of the market for derivative products, most notably forwards,
futures and options, can be traced back to the willingness of risk-averse
economic agents to guard themselves against uncertainties arising out of
fluctuations in asset prices. By their very nature, the financial markets are
marked by a very high degree of volatility. Through the use of derivative
products, it is possible to partially or fully transfer price risks by locking-in asset
prices. As instruments of risk management, these generally do not influence the
fluctuations in the underlying asset prices. However, by locking-in asset prices,
derivative products minimize the impact of fluctuations in asset prices on the
profitability and cash flow situation of risk-averse investors.


Derivative products initially emerged, as hedging devices against fluctuations in
commodity prices and commodity-linked derivatives remained the sole form of
such products for almost three hundred years. The financial derivatives came
into spotlight in post-1970 period due to growing instability in the financial
markets. However, since their emergence, these products have become very
popular and by 1990s, they accounted for about two-thirds of total transactions
in derivative products. In recent years, the market for financial derivatives has
grown tremendously both in terms of variety of instruments available, their
complexity and also turnover. In the class of equity derivatives, futures and
options on stock indices have gained more popularity than on individual stocks,
especially among institutional investors, who are major users of index-linked
derivatives.
Even small investors find these useful due to high correlation of the popular
indices with various portfolios and ease of use. The lower costs associated with
index derivatives vis-vis derivative products based on individual securities is
another reason for their growing use.




                                                                                   4
Derivatives defined
Derivative is a product whose value is derived from the value of one or more
basic variables, called bases (underlying asset, index, or reference rate), in a
contractual manner. The underlying asset can be equity, forex, commodity or
any other asset. For example, wheat farmers may wish to sell their harvest at a
future date to eliminate the risk of a change in prices by that date. Such a
transaction is an example of a derivative. The price of this derivative is driven by
the spot price of wheat which is the “underlying”. In the Indian context the
Securities Contracts (Regulation) Act, 1956 (SC(R) A) defines “equity derivative”
to include –
      1. A security derived from a debt instrument, share, loan whether secured or
          unsecured, risk instrument or contract for differences or any other form of
          security.
      2. A contract, which derives its value from the prices, or index of prices, of
          underlying securities.
The derivatives are securities under the SC(R) A and hence the trading of
derivatives is governed by the regulatory framework under the SC(R) A. 1




1
    Source: www.nse-india.com

                                                                                  5
Factors affecting Financial Derivatives

The following factors have been driving the growth of financial derivatives:
   1. Increased volatility in asset prices in financial markets,
   2. Increased integration of national financial markets with the international
      markets,
   3. Marked improvement in communication facilities and sharp decline in
      their costs,
   4. Development of more sophisticated risk management tools, providing
      economic agents a wider choice of risk management strategies, and
   5. Innovations in the derivatives markets, which optimally combine the risks
      and returns over a large number of financial assets, leading to higher
      returns, reduced risk as well as trans-actions costs as compared to
      individual financial assets.


Types of derivatives
The most commonly used derivatives contracts are forwards, futures and options
which we shall discuss in detail later. Here we take a brief look at various
derivatives contracts that have come to be used.



   1. Forwards
     A forward contract is a customized contract between two entities, where
     settlement takes place on a specific date in the future at today‟s pre-
     agreed price.

   2. Futures
     A futures contract is an agreement between two parties to buy or sell an
     asset at a certain time in the future at a certain price. Futures contracts
     are special types of forward contracts in the sense that the former are
     standardized exchange-traded contracts.



                                                                               6
3. Options
  Options are of two types - calls and puts. Calls give the buyer the right but
 not the obligation to buy a given quantity of the underlying asset, at a given
 price on or before a given future date. Puts give the buyer the right, but
 not the obligation to sell a given quantity of the underlying asset at a given
 price on or before a given date.

4. Swaps
  Swaps are private agreements between two parties to exchange cash flows
 in the future according to a prearranged formula. They can be regarded as
 portfolios of forward contracts. The two commonly used swaps are:
 Interest rate swaps: These entail swapping only the interest related cash
 flows between the parties in the same currency.
 Currency swaps: These entail swapping both principal and interest between
 the parties, with the cash flows in one direction being in a different
 currency than those in the opposite direction.

5. Warrants
  Options generally have lives of up to one year; the majority of options
 traded on options exchanges having a maximum maturity of nine months.
 Longer-dated options are called warrants and are generally traded over-the-
 counter.

6. Leaps
  The acronym LEAPS means Long-Term Equity Anticipation Securities. These
 are options having a maturity of up to three years.
 Baskets: Basket options are options on portfolios of underlying assets. The
 underlying asset is usually a moving average or a basket of assets. Equity
 index options are a form of basket options.




                                                                            7
   7. Swaption
     Swaption are options to buy or sell a swap that will become operative at the
    expiry of the options. Thus a swaption is an option on a forward swap.
    Rather than have calls and puts, the swaption market has receiver swaption
    and payer swaption. A receiver swaption is an option to receive fixed and
    pay floating. A payer swaption is an option to pay fixed and receive
    floating.


Participants and Functions
Three broad categories of participants - hedgers, speculators, and arbitrageurs -
trade in the derivatives market.

    Participants
      1. Hedgers
         Hedgers face risk associated with the price of an asset. They use
         futures or options markets to reduce or eliminate this risk.

      2. Speculators
         Speculators wish to bet on future movements in the price of an asset.
         Futures and options contracts can give them an extra leverage; that is,
         they can increase both the potential gains and potential losses in a
         speculative venture.

      3. Arbitrageurs
         Arbitrageurs are in business to take advantage of a discrepancy
         between prices in two different markets. If, for example, they see the
         futures price of an asset getting out of line with the cash price, they
         will take offsetting positions in the two markets to lock in a profit.




                                                                                  8
 Economic Functions
The derivative market performs a number of economic functions.
   First, prices in an organized derivatives market reflect the perception of
    market participants about the future and lead the prices of underlying to
    the perceived future level. The prices of derivatives converge with the
    prices of the underlying at the expiration of derivative contract. Thus
    derivatives help in discovery of future as well as current prices.
   Second, the derivatives market helps to transfer risks from those who
    have them but may not like them to those who have appetite for them.
   Third, derivatives, due to their inherent nature, are linked to the
    underlying cash markets. With the introduction of derivatives, the
    underlying   market    witnesses   higher    trading   volumes   because   of
    participation by more players who would not otherwise participate for
    lack of an arrangement to transfer risk.
   Fourth, speculative trades shift to a more controlled environment of
    derivatives market. In the absence of an organized derivatives market,
    speculators trade in the underlying cash markets. Margining, monitoring
    and surveillance of the activities of various participants become extremely
    difficult in these kinds of mixed markets.
   Fifth, an important incidental benefit that flows from derivatives trading
    is that it acts as a catalyst for new entrepreneurial activity. The
    derivatives have a history of attracting many bright, creative, well-
    educated people with an entrepreneurial attitude. They often energize
    others to create new businesses, new products and new employment
    opportunities, the benefit of which are immense.
   Sixth, derivatives markets help increase savings and investment in the
    long run. Transfer of risk enables market participants to expand their
    volume of activity. Derivatives thus promote economic development to
    the extent the later depends on the rate of savings and investment.


                                                                               9
Development of exchange-traded derivatives
Derivatives have probably been around for as long as people have been trading
with one another. Forward contracting dates back at least to the 12th century,
and may well have been around before then. Merchants entered into contracts
with one another for future delivery of specified amount of commodities at
specified price.
Although early forward contracts in the US addressed merchants‟ concerns about
ensuring that there were buyers and sellers for commodities, “credit risk”
remained a serious problem. To deal with this problem, a group of Chicago
businessmen formed the Chicago Board of Trade (CBOT) in 1848. The primary
intention of the CBOT was to provide a centralized location known in advance for
buyers and sellers to negotiate forward contracts. In 1865, the CBOT went one
step further and listed the first “exchange traded” derivatives contract in the
US; these contracts were called “futures contracts”. In 1919, Chicago Butter and
Egg Board, a spin-off of CBOT, was reorganized to allow futures trading. Its name
was changed to Chicago Mercantile Exchange (CME). The CBOT and the CME
remain the two largest organized futures exchanges, indeed the two largest
“financial” exchanges of any kind in the world today.


The first stock index futures contract was traded at Kansas City Board of Trade.
Currently the most popular index futures contract in the world is based on S&P
500 index, traded on Chicago Mercantile Exchange. Index futures, futures on T-
bills and Euro-Dollar futures are the three most popular futures contracts traded
today. Other popular international exchanges that trade derivatives are LIFFE in
England, DTB in Germany, SGX in Singapore, TIFFE in Japan, MATIF in France,
etc.




                                                                            10
Exchange-traded vs. OTC derivatives markets
The OTC derivatives markets have witnessed rather sharp growth over the last
few years, which have accompanied the modernization of commercial and
investment banking and globalisation of financial activities. The recent
developments in information technology have contributed to a great extent to
these developments. While both exchange-traded and OTC derivative contracts
offer many benefits, the former have rigid structures compared to the latter. It
has been widely discussed that the highly leveraged institutions and their OTC
derivative positions were the main cause of turbulence in financial markets in
1998. These episodes of turbulence revealed the risks posed to market stability
originating in features of OTC derivative instruments and markets.



    Features of OTC Derivatives market
   The OTC derivatives markets have the following features compared to
exchange-traded derivatives:
   1. The management of counter-party (credit) risk is decentralized and
      located within individual institutions,
   2. There are no formal centralized limits on individual positions, leverage, or
      margining,
   3. There are no formal rules for risk and burden-sharing,
   4. There are no formal rules or mechanisms for ensuring market stability and
      integrity, and for safeguarding the collective interests of market
      participants, and
   5. The OTC contracts are generally not regulated by a regulatory authority
      and the exchange‟s self-regulatory organization, although they are
      affected indirectly by national legal systems, banking supervision and
      market surveillance.




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    Risk associated with OTC Derivatives market

Some of the features of OTC derivatives markets embody risks to financial
market stability. The following features of OTC derivatives markets can give rise
to instability in institutions, markets, and the international financial system:
    The dynamic nature of gross credit exposures
    Information asymmetries
    The effects of OTC derivative activities on available aggregate credit
    The high concentration of OTC derivative activities in major institutions
    The central role of OTC derivatives markets in the global financial system.
      As the asset prices change rapidly, the size and configuration of counter-
      party exposures can become unsustainably large and provoke a rapid
      unwinding of positions.
    Heavy reliance on OTC derivatives creates the possibility of systemic
      financial events, which fall outside the more formal clearing house
      structures.


There has been some progress in addressing these risks and perceptions.
However, the progress has been limited in implementing reforms in risk
management, including counter-party, liquidity and operational risks, and OTC
derivatives markets continue to pose a threat to international financial stability.
Moreover, those who provide OTC derivative products, hedge their risks through
the use of exchange traded derivatives. In view of the inherent risks associated
with OTC derivatives, and their dependence on exchange traded derivatives,
Indian law considers them illegal.




                                                                                   12
Indian Derivatives Market
Starting from a controlled economy, India has moved towards a world where
prices fluctuate every day. The introduction of risk management instruments in
India gained momentum in the last few years due to liberalisation process and
Reserve Bank of India‟s (RBI) efforts in creating currency forward market.
Derivatives are an integral part of liberalisation process to manage risk. NSE
gauging the market requirements initiated the process of setting up derivative
markets in India. In July 1999, derivatives trading commenced in India

    Chronology of instruments

1991                    Liberalisation process initiated.
14 December 1995        NSE asked SEBI for permission to trade index futures.
18 November 1996        SEBI setup L.C.Gupta Committee to draft a policy
                        framework for index futures.
11 May 1998             L.C.Gupta Committee submitted report.
7 July 1999             RBI gave permission for OTC forward rate agreements
                        (FRAs) and interest rate swaps.
24 May 2000             SIMEX chose Nifty for trading futures and options on an
                        Indian index.
25 May 2000             SEBI gave permission to NSE and BSE to do index futures
                        trading.
9 June 2000             Trading of BSE Sensex futures commenced at BSE.
12 June 2000            Trading of Nifty futures commenced at NSE.
25 September 2000       Nifty futures trading commenced at SGX.
2 June 2001             Individual Stock Options & Derivatives




                                                                                13
    Need for derivatives in India today

In less than three decades of their coming into vogue, derivatives markets have
become the most important markets in the world. Today, derivatives have
become part and parcel of the day-to-day life for ordinary people in major part
of the world. Until the advent of NSE, the Indian capital market had no access to
the latest trading methods and was using traditional out-dated methods of
trading. There was a huge gap between the investors‟ aspirations of the markets
and the available means of trading. The opening of Indian economy has
precipitated the process of integration of India‟s financial markets with the
international financial markets. Introduction of risk management instruments in
India has gained momentum in last few years thanks to Reserve Bank of India‟s
efforts in allowing forward contracts, cross currency options etc. which have
developed into a very large market.



Forward contracts & Futures & Options
    Introduction to forward contracts
A forward contract is an agreement to buy or sell an asset on a specified date for
a specified price. One of the parties to the contract assumes a long position and
agrees to buy the underlying asset on a certain specified future date for a
certain specified price. The other party assumes a short position and agrees to
sell the asset on the same date for the same price. Other contract details like
delivery date, price and quantity are negotiated bilaterally by the parties to the
contract. The forward contracts are normally traded outside the exchanges.




                                                                                14
      Features of forward contracts
          The salient features of the forward contract are listed below
           They are bilateral contracts and hence exposed to counter–party
              risk.
             Each contract is custom designed, and hence is unique in terms of
              contract size, expiration date and the asset type and quality.
             The contract price is generally not available in public domain.
             On the expiration date, the contract has to be settled by delivery of
              the asset.
             If the party wishes to reverse the contract, it has to compulsorily go
              to the same counter-party, which often results in high prices being
              charged.


However       forward    contracts   in   certain   markets   have   become     very
standardized, as in the case of foreign exchange, thereby reducing
transaction costs and increasing transactions volume. This process of
standardization reaches its limit in the organized futures market.


Forward contracts are very useful in hedging and speculation. The classic
hedging application would be that of an exporter who expects to receive
payment in dollars three months later. He is exposed to the risk of exchange rate
fluctuations. By using the currency forward market to sell dollars forward, he
can lock on to a rate today and reduce his uncertainty. Similarly an importer who
is required to make a payment in dollars two months hence can reduce his
exposure to exchange rate fluctuations by buying dollars forward.


If a speculator has information or analysis, which forecasts an upturn in a price,
then he can go long on the forward market instead of the cash market. The
speculator would go long on the forward, wait for the price to rise, and then


                                                                                15
take a reversing transaction to book profits. Speculators may well be required to
deposit a margin upfront. However, this is generally a relatively small proportion
of the value of the assets underlying the forward contract. The use of forward
markets here supplies leverage to the speculator.



   Limitations of forward markets
     Forward markets world-wide are afflicted by several problems:
     Lack of centralization of trading
     Illiquidity, and Counter party risk


In the first two of these, the basic problem is that of too much flexibility and
generality. The forward market is like a real estate market in that any two
consenting adults can form contracts against each other. This often makes them
design terms of the deal, which are very convenient in that specific situation,
but makes the contracts non-tradable.


Counterparty risk arises from the possibility of default by any one party to the
transaction. When one of the two sides to the transaction declares bankruptcy,
the other suffers. Even when for-ward markets trade standardized contracts, and
hence avoid the problem of illiquidity, still the counterparty risk remains a very
serious issue.




    Introduction to futures
Futures markets were designed to solve the problems that exist in forward
markets. A futures contract is an agreement between two parties to buy or sell
an asset at a certain time in the future at a certain price. But unlike forward
contracts, the futures contracts are standardized and exchange traded. To
facilitate liquidity in the futures contracts, the exchange specifies certain
standard features of the contract. It is a standardized contract with standard


                                                                             16
underlying instrument, a standard quantity and quality of the underlying
instrument that can be delivered, (or which can be used for reference purposes
in settlement) and a standard timing of such settlement. A futures contract may
be offset prior to maturity by entering into an equal and opposite transaction.
More than 99% of futures transactions are offset this way.




  Standardized items in a futures contract
     Quantity of the underlying
     Quality of the underlying
     The date and the month of delivery
     The units of price quotation and minimum price change
     Location of settlement

  Futures Terminology
  1. Spot price: The price at which an asset trades in the spot market.
  2. Futures price: The price at which the futures contract trades in the futures
      market.
  3. Contract cycle: The period over which a contract trades. The index futures
      contracts on the NSE have one-month, two-month and three-month expiry
      cycles, which expire on the last Thursday of the month. Thus a January
      expiration contract expires on the last Thursday of January and a February
      expiration contract ceases trading on the last Thursday of February. On the
      Friday following the last Thursday, a new contract having a three-month
      expiry is introduced for trading.
  4. Expiry date: It is the date specified in the futures contract. This is the last
      day on which the contract will be traded, at the end of which it will cease
      to exist.
  5. Contract size: The amount of asset that has to be delivered less than one
      contract. For in-stance, the contract size on NSE‟s futures market is 200
      Nifties.


                                                                               17
  6. Basis: In the context of financial futures, basis can be defined as the
     futures price minus the spot price. There will be a different basis for each
     delivery month for each contract. In a normal market, basis will be
     positive. This reflects that futures prices normally exceed spot prices.
  7. Cost of carry: The relationship between futures prices and spot prices can
     be summarized in terms of what is known as the cost of carry. This
     measures the storage cost plus the interest that is paid to finance the asset
     less the income earned on the asset.
  8. Initial margin: The amount that must be deposited in the margin account
     at the time a futures contract is first entered into is known as initial
     margin.
  9. Marking-to-market: In the futures market, at the end of each trading day,
     the margin ac-count is adjusted to reflect the investor‟s gain or loss
     depending upon the futures closing price. This is called marking–to–market.
  10. Maintenance margin: This is somewhat lower than the initial margin. This is
     set to ensure that the balance in the margin account never becomes
     negative. If the balance in the margin account falls below the maintenance
     margin, the investor receives a margin call and is expected to top up the
     margin account to the initial margin level before trading commences on
     the next day.



Introduction to options
In this section, we look at the next derivative product to be traded on the NSE,
namely options. Options are fundamentally different from forward and futures
contracts. An option gives the holder of the option the right to do something.
The holder does not have to exercise this right. In contrast, in a forward or
futures contract, the two parties have committed themselves to doing
something. Whereas it costs nothing (except margin requirements) to enter into
a futures contract, the purchase of an option requires an up–front payment.




                                                                                18
     History of options
Although options have existed for a long time, they were traded OTC, without
much knowledge of valuation. Today exchange-traded options are actively
traded on stocks, stock indexes, foreign currencies and futures contracts. The
first trading in options began in Europe and the US as early as the eighteenth
century. It was only in the early 1900s that a group of firms set up what was
known as the put and call Brokers and Dealers Association with the aim of
providing a mechanism for bringing buyers and sellers together. If someone
wanted to buy an option, he or she would contact one of the member firms.
The firm would then attempt to find a seller or writer of the option either from
its own clients or those of other member firms. If no seller could be found, the
firm would undertake to write the option itself in return for a price. This market
however suffered from two deficiencies. First, there was no secondary market
and second, there was no mechanism to guarantee that the writer of the option
would honor the contract. It was in 1973, that Black, Merton and Scholes
invented the famed Black Scholes formula. In April 1973, CBOE was set up
specifically for the purpose of trading options.



     Option Terminology
   Index options: These options have the index as the underlying. Some options
    are European while others are American. Like index futures contracts, index
    options contracts are also cash settled.
   Stock options: Stock options are options on individual stocks. Options
    currently trade on over 500 stocks in the United States. A contract gives the
    holder the right to buy or sell shares at the specified price.
   Buyer of an option: The buyer of an option is the one who by paying the
    option premium buys the right but not the obligation to exercise his option on
    the seller/writer.




                                                                             19
   Writer of an option: The writer of a call/put option is the one who receives
    the option premium and is thereby obliged to sell/buy the asset if the buyer
    exercises on him.
    There are two basic types of options, call options and put options.
   Call option: A call option gives the holder the right but not the obligation to
    buy an asset by a certain date for a certain price.
   Put option: A put option gives the holder the right but not the obligation to
    sell an asset by a certain date for a certain price.
   Option price: Option price is the price which the option buyer pays to the
    option seller.
   Expiration date: The date specified in the options contract is known as the
    expiration date, the exercise date, the strike date or the maturity.
   Strike price: The price specified in the options contract is known as the
    strike price or the exercise price.
   American options: American options are options that can be exercised at any
    time up to the expiration date. Most exchange-traded options are American.
   European options: European options are options that can be exercised only
    on the expiration date itself. European options are easier to analyze than
    American options, and properties of an American option are frequently
    deduced from those of its European counterpart.
   In-the-money option: An in-the-money (ITM) option is an option that would
    lead to a positive cash flow to the holder if it were exercised immediately. A
    call option on the index is said to be in-the-money when the current index
    stands at a level higher than the strike price (i.e. spot price > strike price). If
    the index is much higher than the strike price, the call is said to be deep ITM.
    In the case of a put, the put is ITM if the index is below the strike price.
   At-the-money option: An at-the-money (ATM) option is an option that would
    lead to zero cash flow if it were exercised immediately. An option on the
    index is at-the-money when the current index equals the strike price (i.e.
    spot price = strike price)._


                                                                                   20
     Out-of-the-money option: An out-of-the-money (OTM) option is an option
      that would lead to negative cash flow it is exercised immediately. A call
      option on the index is out-of- the-money when the current index stands at a
      level which is less than the strike price (i.e. spot price < strike price). If the
      index is much lower than the strike price, the call is said to be deep OTM. In
      the case of a put, the put is OTM if the index is above the strike price.
     Intrinsic value of an option: The option premium can be broken down into
      two components - intrinsic value and time value. The intrinsic value of a call
      is the amount the option is ITM, if it is ITM. If the call is OTM, its intrinsic
      value is zero. Putting it another way, the intrinsic value of a call isN½P which
      means the intrinsic value of a call is Max [0, (S t – K)] which means the
      intrinsic value of a call is the (St – K). Similarly, the intrinsic value of a put is
      Max [0, (K -St)], i.e. the greater of 0 or (K - St). K is the strike price and St is
      the spot price.
     Time value of an option: The time value of an option is the difference
      between its premium and its intrinsic value. A call that is OTM or ATM has
      only time value. Usually, the maximum time value exists when the option is
      ATM. The longer the time to expiration, the greater is a call‟s time value, all
                                                                      2
      else equal. At expiration, a call should have no time value.


Distinction between futures and forwards contracts
Forward contracts are often confused with futures contracts. The confusion is
primarily because both serve essentially the same economic functions of
allocating risk in the presence of future price uncertainty. However futures are a
significant improvement over the forward contracts as they eliminate counter
party risk and offer more liquidity. Table 3.1 lists the distinction between the
two.




2
    Source: www.derivativesindia.com

                                                                                      21
       Futures Vs Forwards

                                              3
Distinction between futures and forwards


Futures                               Forwards
Trade on an organized exchange OTC in nature
Standardized contract terms           Customised contract terms
Hence more liquid                     Hence less liquid
Requires margin payments              No margin payment



Distinction between futures and Options

Futures and options
An interesting question to ask at this stage is - when would one use options
instead of futures? Options are different from futures in several interesting
senses.




       Futures Vs Options

Distinction between futures and options


Futures                            Options
Exchange        traded,      with Same as futures.
novation
Exchange defines the product       Same as futures.
Price is zero, strike price Strike price is fixed, price


3
    Source: Derivatives in India FAQ’s by Ajay Shah & Susan Thomas

                                                                         22
moves                             moves.
Price is zero                     Price is always positive.
Linear payoff                     Nonlinear payoff.
Both long and short at risk       Only short at risk.




At a practical level, the option buyer faces an interesting situation. He pays for
the option in full at the time it is purchased. After this, he only has an upside.
There is no possibility of the options position generating any further losses to him
(other than the funds already paid for the option). This is different from futures,
which is free to enter into, but can generate very large losses. This characteristic
makes options attractive to many occasional market participants, who cannot
put in the time to closely monitor their futures positions.


Buying put options is buying insurance. To buy a put option on Nifty is to buy
insurance, which reimburses the full extent to which Nifty drops below the strike
price of the put option. This is attractive to many people, and to mutual funds
creating “guaranteed return products”. The Nifty index fund industry will find it
very useful to make a bundle of a Nifty index fund and a Nifty put option to
create a new kind of a Nifty index fund, which gives the investor protection
against extreme drops in Nifty.


Index derivatives
Index derivatives are derivative contracts, which derive their value from an
underlying index. The two most popular index derivatives are index futures and
index options. Index derivatives have become very popular worldwide.

    Advantages of Index Derivatives
          o Institutional and       large   equity-holders need   portfolio-hedging
                facility. Index–derivatives are more suited to them and more cost–
                effective than derivatives based on individual stocks. Pension funds



                                                                               23
              in the US are known to use stock index futures for risk hedging
              purposes.
          o Index derivatives offer ease of use for hedging any portfolio
              irrespective of its composition.
          o Stock index is difficult to manipulate as compared to individual
              stock prices, more so in India, and the possibility of cornering is
              reduced. This is partly because an individual stock has a limited
              supply, which can be cornered.
          o Stock index, being an average, is much less volatile than individual
              stock prices. This implies much lower capital adequacy and margin
              requirements.
          o   Index derivatives are cash settled, and hence do not suffer from
              settlement   delays   and   problems    related   to   bad   delivery,
              forged/fake certificates.


Payoff & Pricing of Futures and Options
A payoff is the likely profit/loss that would accrue to a market participant with
change in the price of the underlying asset. This is generally depicted in the form
of payoff diagrams which show the price of the underlying asset on the X–axis
and the profits/losses on the Y–axis. In this section we shall take a look at the
payoffs for buyers and sellers of futures and options.



    Payoff for futures
Futures contracts have linear payoffs. In simple words, it means that the losses
as well as profits for the buyer and the seller of a futures contract are unlimited.
These linear payoffs are fascinating as they can be combined with options and
the underlying to generate various complex payoffs.




                                                                               24
    Payoff for buyer of futures: Long futures
The payoff for a person who buys a futures contract is similar to the payoff for a
person who holds an asset. He has a potentially unlimited upside as well as a
potentially unlimited downside.
Take the case of a speculator who buys a two-month Nifty index futures contract
when the Nifty stands at 1220. The underlying asset in this case is the Nifty
portfolio. When the index moves up, the long futures position starts making
profits, and when the index moves down it starts making losses. Figure 5.1 shows
the payoff diagram for the buyer of a futures contract.


Payoff for a buyer of Nifty futures
The figure shows the profits/losses for a long futures position. The investor
bought futures when the index was at 1220. If the index goes up, his futures
position starts making profit. If the index falls, his futures position starts showing
losses.



  Profit



                                     1220
          0                                             Nifty




  Loss



    Payoff for seller of futures: Short futures
The payoff for a person who sells a futures contract is similar to the payoff for a
person who shorts an asset. He has a potentially unlimited upside as well as a
potentially unlimited downside. Take the case of a speculator who sells a two-
month Nifty index futures contract when the Nifty stands at 1220. The underlying
asset in this case is the Nifty portfolio. When the index moves down, the short

                                                                                 25
futures position starts making profits, and when the index moves up, it starts
making losses. Figure shows the payoff diagram for the seller of a futures
contract.


Payoff for a seller of Nifty futures

The figure shows the profits/losses for a short futures position. The investor sold
futures when the index was at 1220. If the index goes down, his futures position
starts making profit. If the index rises, his futures position starts showing losses.


  Profit



                             1220
         0                                               Nifty


  Loss




    Options payoffs
The optionality characteristic of options results in a non-linear payoff for
options. In simple words, it means that the losses for the buyer of an option are
limited; however the profits are potentially unlimited. For a writer, the payoff is
exactly the opposite. His profits are limited to the option premium; however his
losses are potentially unlimited.
  These non-linear payoffs are fascinating as they lend themselves to be used to
generate various payoffs by using combinations of options and the underlying.
We look here at the six basic payoffs.

    Payoff profile of buyer of asset: Long asset
In this basic position, an investor buys the underlying asset, Nifty for instance,
for 1220, and sells it at a future date at an unknown price,S 4 it is purchased, the



                                                                                 26
investor is said to be “long” the asset. Figure shows the payoff for a long position
on the Nifty.4


Payoff for investor who went Long Nifty at 1220


The figure shows the profits/losses from a long position on the index. The
investor bought the index at 1220. If the index goes up, he profits. If the index
falls he looses.


          Profit
            +60

              0           1160    1220     1280
                                                                       Nifty

             -60


           Loss




       Payoff profile for seller of asset: Short asset
In this basic position, an investor shorts the underlying asset, Nifty for instance,
for 1220, and buys it back at a future date at an unknown price S 4 Once it is sold,
the investor is said to be “short” the asset. Figure shows the payoff for a short
position on the Nifty.




4
    Source: NSE Derivatives Core Module

                                                                               27
Payoff for investor who went Short Nifty at 1220
The figure shows the profits/losses from a short position on the index. The
investor sold the index at 1220. If the index falls, he profits. If the index rises,
he looses.

       Profit


             +60

              0                      1160 1220 1280
                                                           Nifty
          -60
         Loss




    Payoff profile for buyer of call options: Long call
A call option gives the buyer the right to buy the underlying asset at the strike
price specified in the option. The profit/loss that the buyer makes on the option
depends on the spot price of the underlying. If upon expiration, the spot price
exceeds the strike price, he makes a profit. Higher the spot price more is the
profit he makes. If the spot price of the underlying is less than the strike price,
he lets his option expire un-exercised. His loss in this case is the premium he
paid for buying the option. Figure 5.5 gives the payoff for the buyer of a three
month call option (often referred to as long call) with a strike of 1250 bought at
a premium of 86.60.


Payoff for buyer of call option

The figure shows the profits/losses for the buyer of a three-month Nifty 1250 call
option. As can be seen, as the spot Nifty rises, the call option is in-the-money. If
upon expiration, Nifty closes above the strike of 1250, the buyer would exercise
his option and profit to the extent of the difference between the Nifty-close and


                                                                               28
the strike price. The profits possible on this option are potentially unlimited.
However if Nifty falls below the strike of 1250, he lets the option expire. His
losses are limited to the extent of the premium he paid for buying the option.




Profit


                                        1250
     0                                         Nifty

86.60


 Loss




    Payoff profile for writer of call options: Short call
A call option gives the buyer the right to buy the underlying asset at the strike
price specified in the option. For selling the option, the writer of the option
charges a premium. The profit/loss that the buyer makes on the option depends
on the spot price of the underlying. Whatever is the buyer‟s profit is the seller‟s
loss. If upon expiration, the spot price exceeds the strike price, the buyer will
exercise the option on the writer. Hence as the spot price increases the writer of
the option starts making losses. Higher the spot price more is the loss he makes.
If upon expiration the spot price of the underlying is less than the strike price,
the buyer lets his option expire un-exercised and the writer gets to keep the
premium. Below fig gives the payoff for the writer of a three month call option
(often referred to as short call) with a strike of 1250 sold at a premium of 86.60.




                                                                               29
Payoff for writer of call option

The figure shows the profits/losses for the seller of a three-month Nifty 1250 call
option. As the spot Nifty rises, the call option is in-the-money and the writer
starts making losses. If upon expiration, Nifty closes above the strike of 1250, the
buyer would exercise his option on the writer who would suffer a loss to the
extent of the difference between the Nifty-close and the strike price. The loss
that can be incurred by the writer of the option is potentially unlimited, whereas
the maximum profit is limited to the extent of the up-front option premium of
Rs.86.60 charged by him.

Profit

86.60
                                    1250
     0                                                Nifty



 Loss




    Payoff profile for buyer of put options: Long put
A put option gives the buyer the right to sell the underlying asset at the strike
price specified in the option. The profit/loss that the buyer makes on the option
depends on the spot price of the underlying. If upon expiration, the spot price is
below the strike price, he makes a profit. Lower the spot price, more is the
profit he makes. If the spot price of the underlying is higher than the strike
price, he lets his option expire un-exercised. His loss in this case is the premium
he paid for buying the option. Figure 5.7 gives the payoff for the buyer of a three
month put option (often referred to as long put) with a strike of 1250 bought at a
premium of 61.70.

                                                                               30
Payoff for buyer of put option


The figure shows the profits/losses for the buyer of a three-month Nifty 1250 put
option. As can be seen, as the spot Nifty falls, the put option is in-the-money. If
upon expiration, Nifty closes below the strike of 1250, the buyer would exercise
his option and profit to the extent of the difference between the strike price and
Nifty-close. The profits possible on this option can be as high as the strike price.
However if Nifty rises above the strike of 1250, he lets the option expire. His
losses are limited to the extent of the premium he paid for buying the option.


Profit


                                    1250
     0
61.70                                           Nifty



 Loss




    Payoff profile for writer of put options: Short put
A put option gives the buyer the right to sell the underlying asset at the strike
price specified in the option. For selling the option, the writer of the option
charges a premium. The profit/loss that the buyer makes on the option depends
on the spot price of the underlying. Whatever is the buyer‟s profit is the seller‟s
loss. If upon expiration, the spot price happens to be below the strike price, the
buyer will exercise the option on the writer. If upon expiration the spot price of
the underlying is more than the strike price, the buyer lets his option expire un-
exercised and the writer gets to keep the premium. Figure 5.8 gives the payoff



                                                                               31
for the writer of a three-month put option (often referred to as short put) with a
strike of 1250 sold at a premium of 61.70.


Payoff for writer of put option
The figure shows the profits/losses for the seller of a three-month Nifty 1250 put
option. As the spot Nifty falls, the put option is in-the-money and the writer
starts making losses. If upon expiration, Nifty closes below the strike of 1250,
the buyer would exercise his option on the writer who would suffer a loss to the
extent of the difference between the strike price and Nifty-close. The loss that
can be incurred by the writer of the option is a maximum extent of the strike
price(Since the worst that can happen is that the asset price can fall to zero)
whereas the maximum profit is limited to the extent of the up-front option
premium of Rs.61.70 charged by him.

Profit

61.70
                                   1250
     0                                               Nifty




 Loss


Pricing
    Pricing Index Futures
   Stock index futures began trading on NSE on the 12th June 2000. Ever since,
   the volumes and open interest has been steadily growing. Looking at the
   futures prices on NSE‟s market, have you ever felt the need to know whether
   the quoted prices are a true reflection of the underlying index‟s price? Have
   you wondered whether you could make risk-less profits by arbitraging
   between the underlying and futures markets? If so, you need to know the




                                                                             32
   cost-of-carry to understand the dynamics of pricing that constitute the
   estimation of fair value of futures.


   The cost of carry model
   We use fair value calculation of futures to decide the no-arbitrage limits on
   the price of a futures contract. This is the basis for the cost-of-carry model
   where the price of the contract is defined as:
                                          F=S+C
   Where:
   F: Futures price
   S: Spot price
   C: Holding costs or carry costs
   This can also be expressed as:
                                                   T
                                       F=s (1+r)
   Where:
   r: Cost of financing
   T: Time till expiration


                    T
   If F < s (1+r)       or F > s (1+r) T, arbitrage opportunities would exist i.e.
   whenever the futures price moves away from the fair value, there would be
   chances for arbitrage. We know what the spot and future prices are, but what
   are the components of holding cost? The components of holding cost vary
   with contracts on different assets. At times the holding cost may even be
   negative. In the case of commodity futures, the holding cost is the cost of
   financing plus cost of storage and insurance purchased etc. In the case of
   equity futures, the holding cost is the cost of financing minus the dividends
   returns.


Note: In the futures pricing examples worked out in this book, we are using the
concept of discrete compounding, where interest rates are compounded at
discrete intervals, for example, annually or semiannually. Pricing of options and

                                                                             33
other complex derivative securities requires the use of continuously compounded
interest rates. Most books on derivatives use continuous compounding for pricing
futures too. However, we have used discrete compounding as it is more intuitive
and simpler to work with. Had we to use the concept of continuous
compounding, the above equation would have been expressed as:
                                                   rT
                                           F= Se
Where:
r: Cost of financing (using continuously compounded interest rate)
T: Time till expiration
e: 2.71828



    Pricing futures contracts on commodities
Let us take an example of a futures contract on a commodity and work out the
price of the contract. The spot price of silver is Rs.7000/kg. If the cost of
financing is 15% annually, what should be the futures price of 100 Gms of silver
one month down the line? Let us assume that we‟re on 1st January 2001. How
would we compute the price of a silver futures contract expiring on 30th
January? From the discussion above we know that the futures price is nothing but
the spot price plus the cost-of-carry. Let us first try to work out the components
of the cost-of-carry model.


1. What is the spot price of silver? The spot price of silver, S= Rs.7000/kg.
                                                                  30/365
2. What is the cost of financing for a month? (1+0.15)
3. What are the holding costs? Let us assume that the storage cost = 0.
In this case the fair value of the futures price, works out to be = Rs.708.
                          F=s (1+r) T + C = 700(1.15)   30/365
                                                                 =Rs. 708
If the contract was for 3 month period i.e. expiring 30 th March the cost of
financing would increase the futures price. Therefore, the futures price would be
                90/365
C = 700(1.15)            = Rs.724.5. On the other hand, if the one-month contract was
for 10,000 kg. Of silver instead of 100 Gms, then it would involve a non-zero


                                                                                34
storage cost, and the price of the future contract would be Rs. 708 +the cost of
storage.



     Pricing futures contracts on equity index
A futures contract on the stock market index gives its owner the right and
obligation to buy or sell the portfolio of stocks characterized by the index. Stock
index futures are cash settled; there is no delivery of the underlying stocks.


In their short history of trading, index futures have had a great impact on the
world‟s securities markets. Indeed, index futures trading have been accused of
making the world‟s stock markets more volatile than ever before. The critics
claim that individual investors have been driven out to the equity markets
because the actions of institutional traders in both the spot and futures markets
cause stock values to gyrate with no links to their fundamental values. Whether
stock index futures trading is a blessing or a curse is debatable. It is certainly
true, however, that its existence has revolutionized the art and science of
institutional equity portfolio management.


The main differences between commodity and equity index futures are that: _
   There are no costs of storage involved in holding equity.
   Equity comes with a dividend stream, which is a negative cost if you are long
    the stock and positive costs if you are short the stock.
Therefore, Cost of carry = Financing cost - Dividends
Thus, a crucial aspect of dealing with equity futures as opposed to commodity
futures is an accurate forecasting of dividends. The better the forecast of
dividend offered by a security, the better is the estimate of the futures price.




                                                                                 35
    Pricing index futures given expected dividend amount
The pricing of index futures is also based on the cost-of-carry model, where the
carrying cost is the cost of financing the purchase of the portfolio underlying the
index, minus the present value of dividends obtained from the stocks in the
index portfolio.
Example
Nifty futures trade on NSE as one, two and three-month contracts. What will be
the price of a new two-month futures contract on Nifty?


1. Let us assume that M & M will be declaring a dividend of Rs. 10 per share after
15 days of purchasing the contract.
2. Current value of Nifty is 1200 and Nifty trades with a multiplier of 200.
3. Since Nifty is traded in multiples of 200, value of the contract is 200*1200 =
Rs.240, 000.
4. If M & M has a weight of 7% in Nifty, its value in Nifty is Rs.16,800 i.e.(240,000
* 0.07).
5. If the market price of M & M is Rs.140, then a traded unit of Nifty involves 120
shares of M & M i.e.(16,800/140).
6. To calculate the futures price, we need to reduce the cost-of-carry to the
extent of dividend received. The amount of dividend received is Rs.1200 i.e.(120
* 10). The dividend is received 15 days later and hence compounded only for the
remainder of 45 days. To calculate the futures price we need to compute the
amount of dividend received per unit of Nifty. Hence we divide the compounded
dividend figure by 200.
                                        60/365                   45/365
7. Thus, futures price F = 1200(1.15)            {120*10(1.15)            /200} =Rs. 1221.80



    Pricing index futures given expected dividend yield
If the dividend flow throughout the year is generally uniform, i.e. if there are
few historical cases of clustering of dividends in any particular month, it is useful
to calculate the annual dividend yield.


                                                                                        36
                                    F = s (1+r-q) T
Where:
F: futures price    S: spot index value r: cost of financing
q: expected dividend yield     T: holding period


Example
A two-month futures contract trades on the NSE. The annual dividend yield on
Nifty is 2% annualized. The spot value of Nifty 1200. What is the fair value of the
futures contract?
                                 60/365
Fair value = 1200(1+.015-0.02)            =Rs. 1224.35


The cost of carry model explicitly defines the relationship between the futures
price and the related spot price. As we know, the difference between the
futures price and the spot price is called the basis.
Nuances
   As the date of expiration comes near, the basis reduces - there is a
    convergence of the futures price towards the spot price. On the date of
    expiration, the basis is zero. If it is not, then there is an arbitrage
    opportunity. Arbitrage opportunities can also arise when the basis (difference
    between spot and futures price) or the spreads (difference between prices of
    two futures contracts) during the life of a contract are incorrect. At a later
    stage we shall look at how these arbitrage opportunities can be exploited.
   There is nothing but cost-of-carry related arbitrage that drives the behavior
    of the futures price.
   Transactions costs are very important in the business of arbitrage.



     Pricing options
An option buyer has the right but not the obligation to exercise on the seller.
The worst that can happen to a buyer is the loss of the premium paid by him. His
downside is limited to this premium, but his upside is potentially unlimited. This


                                                                              37
optionally is precious and has a value, which is expressed in terms of the option
price. Just like in other free markets, it is the supply and demand in the
secondary market that drives the rice of an option. On dates prior to 31 Dec
2000, the “call option on nifty expiring on 31 Dec 2000 with a strike of 1500” will
trade at a price that purely reflects supply and demand. There is a separate
order book for each option which generates its own price. The values shown in
Table 5.1 are derived from a theoretical model, namely the Black-Scholes option
pricing model. If the secondary market prices deviate from these values, it would
imply the presence of arbitrage opportunities, which (we might expect) would be
swiftly exploited. But there is nothing innate in the market, which forces the
prices in the table to come about.


There are various models, which help us get close to the true price of an option.
Most of these are variants of the celebrated Black-Scholes model for pricing
European options. Today most calculators and spreadsheets come with a built-in
Black-Scholes options pricing formula so to price options we don‟t really need to
memorize the formula. What we shall do here is discuss this model in a fairly
non-technical way by focusing on the basic principles and the underlying
intuition.



       Introduction to the Black–Scholes formulae
       Intuition would tell us that the spot price of the underlying, exercise
       price, risk-free interest rate, volatility of the underlying, time to
       expiration and dividends on the underlying (stock or index) should affect
       the option price. Interestingly before Black and Scholes came up with
       their option pricing model, there was a widespread belief that the
       expected growth of the underlying ought to affect the option price. Black
       and Scholes demonstrate that this is not true. The beauty of the Black and
       Scholes model is that like any good model, it tells us what is important
       and what is not. It doesn‟t promise to


                                                                              38
Option prices: some illustrative values


          Option strike price

              1400          1450           1500          1550           1600
Calls
  1 mth       117           79             48            27             13

   3 mth      154           119           90             67             48
Puts
   1 mth      8             19            38             66             102
   3 mth      25            39            59             84             114
Assumptions: Nifty spot is 1500, Nifty volatility is 25% annualized,   interest rate
is 10%, and Nifty dividend yield is 1.5%.

Produce the exact prices that show up in the market, but definitely does a
remarkable job of pricing options within the framework of assumptions of
the model. Virtually all option pricing models, even the most complex
ones, have much in common with the Black–Scholes model.


Black and Scholes start by specifying a simple and well–known equation
that models the way in which stock prices fluctuate. This equation called
Geometric Brownian Motion, implies that stock returns will have a
lognormal distribution, meaning that the logarithm of the stock‟s re-turn
will follow the normal (bell shaped) distribution. Black and Scholes then
propose that the option‟s price is determined by only two variables that
are allowed to change: time and the underlying stock price. The other
factors - the volatility, the exercise price, and the risk–free rate do affect
the option‟s price but they are not allowed to change. By forming a
portfolio consisting of a long position in stock and a short position in calls,
the risk of the stock is eliminated. This hedged portfolio is obtained by
setting the number of shares of stock equal to the approximate change in
the call price for a change in the stock price. This mix of stock and calls
must be revised continuously, a process known as delta hedging.



                                                                             39
Black and Scholes then turn to a little–known result in a specialized field
of probability known as stochastic calculus. This result defines how the
option price changes in terms of the change in the stock price and time to
expiration. They then reason that this hedged combination of options and
stock should grow in value at the risk–free rate. The result then is a
partial differential equation. The solution is found by forcing a condition
called a boundary condition on the model that requires the option price to
converge to the exercise value at expiration. The end result is the Black
and Scholes model.


The Black–Scholes option pricing formulae
The Black–Scholes formulas for the prices of European calls and puts on a
non-dividend paying stock are:


C = SN(d1) – Xe-rT N(d2)
P = Xe-rT N(-d2)- SN(-d1)
Where d1 = [ ln s/x +(r+δ2/2)T ]/ δ √T
And d2 = d1 –δ√T


   The Black Scholes equation is done in continuous time. This requires
    continuous compounding. The “r” that in this is in (1+r). E.g. if the
    interest rate per annum is 12%, you need to use ln1.12 or 0.1133,
    which is continuously compounded equivalent of 12% per annum.
   N () is the cumulative normal distribution. N (d1) is called the delta of
    the option which is a measure of change in option in option price with
    respect to change in the price of the underlying asset.
   δ a measure of volatility is the annualized standard deviation of
    continuously compounded returns on the underlying. When daily sigma
    is given, they need to be converted into annualized sigma.
   Σ   annual   =Σ   daily   * √number of trading days per year. On a average there
    are 250 trading days in a year.

                                                                               40
         X is the exercise price; S is the spot price and T the time to expiration.



    Pricing index options
Under the assumptions of the Black–Scholes options pricing model, index options
should be valued in the same way as ordinary options on common stock. The
assumption is that investors can costlessly purchase the underlying stocks in the
exact amount necessary to replicate the index; that is, stocks are infinitely
divisible and that the index follows a diffusion process such that the continuously
compounded returns distribution of the index is normally distributed. To use the
Black–Scholes formula for index options, we must however make adjustments for
the dividend payments received on the index stocks. If the dividend payment is
sufficiently smooth, this merely involves replacing the current index value S in
the model with Se-qT where q is the annual dividend yield and T is the time to
expiration in years.


The Black-Scholes formula is so commonly used that it comes programmed into
most calculators and spreadsheets. Hence it is not necessary to memorize the
formula. One only needs to know how to use it.
Note: The pricing models discussed in this chapter give an approximate idea
about the true options price. However the price observed in the market is the
outcome of the price–discovery mechanism (demand–supply principle) and may
differ from the so-called true price.


SWAPS
A contract between two parties, referred to as counter parties, to exchange two
streams of payments for agreed period of time. The payments, commonly called
legs or sides, are calculated based on the underlying notional using applicable
rates. Swaps contracts also include other provisional specified by the counter
parties. Swaps are not debt instrument to raise capital, but a tool used for
financial management. Swaps are arranged in many different currencies and
different periods of time. US$ swaps are most common followed by Japanese

                                                                                41
yen, sterling and Deutsche marks. The length of past swaps transacted has
ranged from 2 to 25 years.




    Why did swaps emerge?
In the late 1970's, the first currency swap was engineered to circumvent the
currency control imposed in the UK. A tax was levied on overseas investments to
discourage capital outflows. Therefore, a British company could not transfer
funds overseas in order to expand its foreign operations without paying sizeable
penalty. Moreover, this British company had to take an additional currency risks
arising from servicing a sterling debt with foreign currency cash flows. To
overcome such a predicament, back-to-back loans were used to exchange debts
in different currencies. For example, a British company wanting to raise capital
in the France would raise the capital in the UK and exchange its obligations with
a French company, which was in a reciprocal position. Though this type of
arrangement was providing relief from existing protections, one could imagine,
the task of locating companies with matching needs was quite difficult in as
much as the cost of such transactions was high. In addition, back-to-back loans
required drafting multiple loan agreements to state respective loan obligations
with clarity. However this type of arrangement leads to development of more
sophisticated swap market of today.
Facilitators
The problem of locating potential counter parties was solved through dealers and
brokers. A swap dealer takes on one side of the transaction as counterparty.
Dealers work for investment, commercial or merchant banks. "By positioning the
swap", dealers earn bid-ask spread for the service. In other words, the swap
dealer earns the difference between the amount received from a party and the
amount paid to the other party. In an ideal situation, the dealer would offset his
risks by matching one step with another to streamline his payments. If the dealer
is a counterparty paying fixed rate payments and receiving floating rate
payments, he would prefer to be a counterparty receiving fixed payments and


                                                                             42
paying floating rate payments in another swap. A perfectly netted position as
just described is not necessary. Dealers have the flexibility to cover their
exposure by matching multiple parties and by using other tools such as futures to
cover an exposed position until the book is complete.


Swap brokers, unlike a dealer do not take on a swap position themselves but
simply locate counter parties with matching needs. Therefore, brokers are free
of any risks involved with the transactions. After the counter parties are located,
the brokers negotiate on behalf of the counter parties to keep the anonymity of
the parties involved. By doing so, if the swap transaction falls through, counter
parties are free of any risks associated with releasing their financial information.
Brokers receive commissions for their services.



       Swaps Pricing:
There are four major components of a swap price.
     Benchmark price
     Liquidity (availability of counter parties to offset the swap).
     Transaction cost
     Credit risk 5


Swap rates are based on a series of benchmark instruments. They may be quoted
as a spread over the yield on these benchmark instruments or on an absolute
interest rate basis. In the Indian markets the common benchmarks are MIBOR,
14, 91, 182 & 364 day T-bills, CP rates and PLR rates.
Liquidity, which is function of supply and demand, plays an important role in
swaps pricing. This is also affected by the swap duration. It may be difficult to
have counter parties for long duration swaps, especially so in India Transaction
costs include the cost of



5
    Source: www.appliederivatives.com

                                                                               43
Hedging a swap: - Say in case of a bank, which has a floating obligation of 91
days T. Bill. Now in order to hedge the bank would go long on a 91 day T. Bill.
For doing so the bank must obtain funds. The transaction cost would thus involve
such a difference.
Yield on 91 day T. Bill - 9.5%
Cost of fund (e.g. - Repo rate) – 10%
The transaction cost in this case would involve 0.5%
Credit risk must also be built into the swap pricing. Based upon the credit rating
of the counterparty a spread would have to be incorporated. Say for e.g. it
would be 0.5% for an AAA rating.



    Swap Market Participation’s
Since swaps are privately negotiated products, there is no restriction on who can
use the market. However, parties with low credit quality have difficulty entering
the market. This is due to fact that they cannot be matched with counter parties
who are willing to take on their risks. In the U.S. many parties require their
counter parties to have minimum assets of $10 million. This requirement has
become a standardized representation of "eligible swap participants".



    Currency Swaps in India
RBI in its slack season credit policy '97 allowed the authorized dealers to arrange
currency swap without its prior approval. This was to enable those requiring
long-term forward cover to hedge themselves without altering the external
liability of the country. Prior to this policy RBI had been approving rupee foreign
currency swaps between corporates on a case basis, but no such swaps were
taking place.


RBI in its process of making the Indian corporates globally competitive has
simplified their access to this instrument by making changes in its credit policy.
But despite an easing regulation, swaps have not hit the market in a big way.

                                                                                44
India has a strong dollar-rupee forward market with contracts being traded for
one, two, six-month expiration. Daily trading volume on this forward market is
around $500 million a day. Indian users of hedging services are also allowed to
buy derivatives involving other currencies on foreign markets. Outside India,
there is a small market for cash –settled forward contracts on the dollar –rupee
exchange rate.


While studying swaps in the Indian context, the counter parties involved are
Indian corporates and the swap dealers are the Authorized dealers of foreign
exchange, i.e., the banks allowed by RBI to carry out the swaps. These banks
form the counterparty to the corporates on both sides of the swap and keep a
spread between the interest rates to be received and offered. One of the
currencies involved is the Indian rupee and the other could be any foreign
currency. The interest rate on the rupee is most likely to be fixed, and on
foreign currency it could be either fixed or floating.



    The Players
Swaps are instruments, which allow the user to hedge - that are to offset risk or
to take risk deliberately in the expectation of making profit. The user in this
case would be any corporate having a foreign exchange exposure/ a risk. A
foreign exchange exposure will arise out of the mismatch between the currency
of inflow and outflow. The outflow being considered here is the interest and the
principal payment on the borrowings of the corporate. Corporate having such
currency mismatches would be of the following types


   1. Corporate with rupee loan and forex revenue
      Mainly the exporters would fall in this category. Corporate with foreign
      subsidiaries would also be having forex revenues but due to cheaper
      availability of funds abroad, it is unlikely that these subsidiaries would be


                                                                              45
      funded by a rupee loan. Thus the main players meeting this criterion
      would be the exporters. The main players in the Indian market are Tata
      Exports, Hindustan Levers Ltd., ITC Ltd., and Nestle Indian Ltd. among the
      others.


   2. Corporate with forex loan and rupee revenue
      The corporate having foreign currency loan could further be classified into
      two groups. One which have net imports and thus may have raised loans to
      meet their import requirements, for example Bharat Heavy Electricals
      Ltd., Apollo Tyres Ltd., Tata Power Co. Ltd.
      Two, which do not have net imports but have raised foreign currency loan
      for funding requirements, for example Arvind Mills Ltd., Ballarpur
      Industries etc.


   3. Corporate with no foreign exposure
There may be corporate with no existing exposure but willing to take up an
exposure in an expectation of making profit out of this transaction. Thus they
would be willing to swap their rupee loan with forex loan and book in forward
cover or make the payments on spot basis on the day of disbursements. These
corporates may also consider the option of raising new loans in foreign currency
and swap a rupee loan if it turns out to be cheaper option. Thus many corporates
would fall under this Bank category. They act as the authorized dealers and are
instrumental in arranging swaps. They have to take the swaps on their books. A
bank would enter into swap with a party and then try to find another with
opposite requirement to hedge itself against any fluctuation in exchange rates.
They would normally keep a spread between the offer and bid rate thus make
profit from transaction. They also take up the credit risk of counterparties.




                                                                                46
    Currency swaps meets the player needs
       1. To manage the exchange rate risk
Since the international trade implies returns and payments in a variety of
currencies whose relative values may fluctuate it involves taking foreign
exchange risk. The players mentioned above are facing this risk. A key question
facing the players then is whether these exchange risks are so large as to affect
their business. A related question is what, if any, special strategies should be
followed to reduce the impact of foreign exchange risk.
One-way to minimize the long-term risk of one currency being worth more or less
in the future is to offset the particular cash flow stream with an opposite flow in
the same currency. The currency swap helps to achieve this without raising new
funds; instead it changes existing cash flows.


           2. To lower financing cost
Currency swaps can be used to reduce the cost of loan. The following example
deals with such a case.
Consider two Indian corporate A & B. Corporate A is an exporter with a rupee
loan at 14% fixed rate. B has a dollar loan at LIBOR + 0.25% floating rate. Due to
difference in the credit rating of the two companies, the rates at which the loans
are available to them are different. A has access to 14% rupee loan and dollar
loan at LIBOR + 0.25%.
A would like to convert its rupee loan into a dollar loan, to reverse its revenue in
dollars and B would like to convert the dollar loan into a fixed rupee loan thus
crystallizing its cost of borrowing. They can enter into a swap and reduce the
cost compared to what it would have been if they had taken a direct loan in the
desired currencies.
Comparative advantage
Company A Exporter                               Company B
Options:                                         Options:
Borrow rupee at 13%                              Borrow rupee at 14.5%



                                                                               47
Borrow dollars at LIBOR +100 bps                    Borrow dollars at LIBOR +200
bps


Company A has an absolute advantage over B in both the markets/ rates. The
advantage in terms of rupee funds is 150 bps while it is 100 bps in case of
dollar rates. Thus B has a comparative advantage in terms of dollar rates.
Now as A is an exporter he would be more interested in a dollar denominated
loan to offset his future receivables.
Therefore it would be advantageous if A would borrow at rupee rates and B
borrows at LIBOR rates. Then they may go in for a currency swap. The net gain
arising out of such a swap will be 50 bps, which may be shared between the
parties.
The swap will thus result in A paying B a floating rate of LIBOR + 75 bps in
return for a 13% fixed rupee rate. The swap will take place on a notional
principal basis. The effective cost for A is LIBOR + 75 bps and for B it is 14.25%.
The effective cost for A is 12.75%. This results into a net saving of 25 bps for
both the parties


.
                           LIBOR +75 bps

        Company A                               Company B
                           12.75% in INR


      13% in INR                                   Libor +200 bps



           3. To access restricted markets
Many countries have restrictions on the type of borrowers that can raise funds
in their bond markets. Foe example an Indian firm exporting goods to Japan
may wish to issue bonds in yen to form a natural hedge by reversing their cash
flows. To issue a yen bond, the borrower must qualify for a single A credit


                                                                                48
rating. If the company does not qualify in this regard it would fail to issue yen
denominated bond.
By issuing bonds in the rupee market and then entering into a currency swap,
the firm can meet its expectation of raising a yen denominated loan.


          4. Swaps for reducing the cost of borrowing
With the introduction of rupee derivatives the Indian corporates can attempt to
reduce their cost of borrowing and thereby add value. A typical Indian case
would be a corporate with a high fixed rate obligation.
Eg. Mehta Ltd. an AAA rated corporate, 3 years back had raised 4-year funds at
a fixed rate of 18.5%. Today a 364-day T. bill is yielding 10.25%, as the interest
rates have come down. The 3-month MIBOR is quoting at 10%.


Fixed to floating 1 year swaps are trading at 50 bps over the 364-day T. bill vs
6-month MIBOR. The treasurer is of the view that the average MIBOR shall
remain below 18.5% for the next one year.


The firm can thus benefit by entering into an interest rate fixed for floating
swap, whereby it makes floating payments at MIBOR and receives fixed
payments at 50 bps over a 364 day treasury yield i.e. 10.25 + 0.50 = 10.75 %.




                           Fixed 10.75
      Mehta Ltd                                                Counter Party

                            3 Months MIBOR

             18.75%s                                   MIBOR




                                                                                 49
The effective cost for Mehta Ltd. = 18.5 + MIBOR - 10.75
                                                = 7.75 + MIBOR
At the present 3m MIBOR at 10%, the effective cost is = 10 + 7.75 = 17.75%


The gain for the firm is (18.5 - 17.75) = 0.75 %


The risks involved for the firm are
- Default/ credit risk of counterparty. This may be ignored, as the counterparty
is a bank. This risk involves losses to the extent of the interest rate differential
between fixed and floating rate payments.
- The firm is faced with the risk that the MIBOR goes beyond 10.75%. Any rise
beyond 10.75% will raise the cost of funds for the firm. Therefore it is very
essential that the firm hold a strong view that MIBOR shall remain below
10.75%. This will require continuous monitoring on the path of the firm.


How does the bank benefit out of this transaction?
The bank either goes for another swap to offset this obligation and in the
process earn a spread. The bank may also use this swap as an opportunity to
hedge its own floating liability. The bank may also leave this position
uncovered if it is of the view that MIBOR shall rise beyond 10.75%.


Taking advantage of future views/ speculation
If a bank holds a view that interest rate is likely to increase and in such a case
the return on fixed rate assets will not increase, it will prefer to swap it with a
floating rate interest. It may also swap floating rate liabilities with a fixed
rate.




                                                                                  50
    Factors to be looked at while doing a swap
Though swaps can be used in the above conditions effectively, corporate need
to look at a few factors before deciding to swap.

      1. The estimated net exposure
   They need to estimate the net exposure that they are likely to have in the
   future. Projecting the growth in exports/ imports, taking into account the
   changes in management and government policies can do this.
   Expected range of exchange rates
   This can be determined by a fundamental and technical analysis. For
   fundamental analysis one needs to keep track of the balance of payment
   condition, GDP growth rate, etc. of the country. The technical factors look
   at past trends and expected demand-supply position. Other factors like
   political stability also need to be considered.

   2. Expected interest rates
      Since currency swaps include exchange of interest payments, the
      interest rates also need to be traced. By keeping an eye on the yield
      curve of long term bonds and the macro economic variables of different
      countries, the interest rates can be estimated.

   3. Amount of cover to be taken
      Having estimated the amount of exposure, the expected exchange rates
      and the interest rates, the parties can determine the risks involved and
      can decide upon the amount of cover to be taken. This shall depend on
      the management policy whether they believe in minimizing the risk for a
      given level of return or maximizing the gain for a given level of risk. The
      risk taking capability of a corporate will depend upon the financial
      backup to absorb the losses, if any, the availability of time and
      resources to monitor the forex market.



                                                                              51
Introduction of Forward Rate Agreements and Interest
Rate Swaps
    Objective
      To further deepen the money markets
      To enable banks, primary dealers and all India financial institutions to
       hedge interest rate risks.


These guidelines are intended to form the basis for development of Rupee
derivative products such as FRAs/IRS in the country. They have been
formulated in consultation with market participants. The guidelines are subject
to review, on the basis of development of FRAs/IRS market.
Accordingly, it has been decided to allow scheduled commercial banks
(excluding Regional Rural Banks), primary dealers and all -India financial
institutions to undertake FRAs/IRS as a product for their own balance sheet
management and for market making purposes.
Prerequisites
Participants are to ensure that appropriate infrastructure and risk management
systems are put in place. Further, participants should also set up sound internal
control system whereby a clear functional separation of trading, settlement,
monitoring and control and accounting activities is provided.




                                                                              52
 Description of the product
         Forward Rate Agreement
         A Forward Rate Agreement (FRA) is a financial contract between
         two parties exchanging or swapping a stream of interest payments
         for a notional principal amount on settlement date, for a
         specified period from start date to maturity date. Accordingly, on
         the settlement date, cash payments based on contract (fixed) and
         the settlement rate, are made by the parties to one another. The
         settlement   rate   is   the   agreed   benchmark/reference   rate
         prevailing on the settlement date.

         Interest Rate Swap
         An Interest Rate Swap (IRS) is a financial contract between two
         parties exchanging or swapping a stream of interest payments for
         a notional principal amount of multiple occasions on specified
         periods. Accordingly, on each payment date that occurs during
         the swap period-Cash payments based on fixed/floating and
         floating rates are made by the parties to one another.
         Currency swaps can be defined as a legal agreement between two
         or more parties to exchange interest obligation or interest
         receipts between two different currencies. It involves three steps:
        Initial exchange of principal between the counter parties at an
         agreed upon rate of exchange which is usually based on spot
         exchange rate. This exchange is optional and its sole objective is
         to establish the quantum of the respective principal amounts for
         the purpose for calculating the ongoing payments of interest and
         to establish the principal amount to be re-exchanged at the
         maturity of the swap.
        Ongoing exchange of interest at the rates agreed upon at the
         outset of the transaction.



                                                                         53
             Re-exchange of principal amount on maturity at the initial rate of
              exchange.



Market Report- Issues of Concern
Unfortunately, money markets as a whole are not developed. The biggest
problem continues to be the structure of the money market. Two-way quotes
are a fundamental necessity for a proper yield curve to develop and a
reference rate to be established. The RBI does not encourage lend/borrow
transaction on the same day. While foreign banks and some of the new banks
are perennial borrowers in the inter-bank market, several nationalised banks
and institutions are perennial lenders. This leaves the primary dealers to do the
trading. But their limited funds do not enable them to become large players.
This gives rise to uni-directional players who are averse to two-way quotes.
This deters the development of a benchmark around which a term market can
evolve.
Right now, whatever trading is done is through the fixed rate. For IRS to
happen there should be swaps in maturities. A benchmarking has to be done
and for that we need a correct reference rate, which will have to evolve
beyond the overnight rate (MIBOR). That can happen only if a term money
market is in place.


In India fixed rates are aplenty with banks and institutions borrowing and
lending at fixed rates. They also adopt floating rates (Prime Lending Rate or
PLR) while lending. But the PLR has two crucial deficiencies compared to rates


Like LIBOR: PLR is not a market related rate, but determined, somewhat
arbitrarily, on the basis of the bank rate. Besides there are no two-way quotes
in PLR, in the absence of which swap deals virtually become in fructuous. Rates
like LIBOR, Fed Funds Rate/ T-Bill Rate are those at which banks are prepared
to lend and borrow in any currency.


                                                                              54
In India too, such a market does exist for the rupee- the call money market.
Banks borrow/lend at market determined rates. But where the Indian money
market differs from other major financial centers is that, in the latter money is
available for periods ranging from 1 or 7 days to 3, 6 and 12 months, whereas in
India, rupee is available for a day or two, up to a maximum period of 13 days,
as a general rule. The reason being the fortnightly reserve requirements.


Another deficiency is the lack of integration with the foreign exchange (FX)
markets. In order to protect and control the exchange rate of the rupee, strong
silos have been created. Forward premium between the rupee and another
foreign currency does not reflect the interest rate differential. If anything, it
reflects the estimated risk of depreciation of the local unit against the dollar.
This gives rise to significant arbitrage opportunities between the two markets,
which are protected through the RBI diktat. At present, the tenors available in
the IRS market are short and the benchmark limited to only one, the Mumbai
Inter-bank Offer Rate (MIBOR).




                                                                              55
Bibliography

  Books
1. Options Futures, and other Derivatives by John C Hull
2. NSE‟s Certification in Financial Markets: - Derivatives Core module


Websites
1. www.derivativesindia.com
2. www.nse-india.com
3. www.sebi.gov.in
4. www.rediff/money/derivatives.htm
5. www.iinvestor.com
6. www.appliederivatives.com
7. www.erivativesreview.com
8. www.economictimes.com
9. www.cboe.com (Chicago Board of Exchange)
10. www.adtading.com
11. www.numa.org




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