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					          Topic 1
Introduction To Derivatives

   This first lecture has four main goals:
    1.   Introduce you to the notion of risk and the role of derivatives in
         managing risk.
            Discuss some of the general terms – such as short/long positions,
             bid-ask spread – from finance that we need.

    2.   Introduce you to three major classes of derivative securities.
            Forwards
            Futures
            Options

    3.   Introduce you to the basic viewpoint needed to analyze these

    4.   Introduce you to the major traders of these instruments.
   Finance is the study of risk.
       How to measure it
       How to reduce it
       How to allocate it

   All finance problems ultimately boil down to three main
       What are the cash flows, and when do they occur?
       Who gets the cash flows?
       What is the appropriate discount rate for those cash flows?

   The difficulty, of course, is that normally none of those
    questions have an easy answer.
   As you know from other classes, we can generally classify risk as
    being diversifiable or non-diversifiable:
        Diversifiable – risk that is specific to a specific investment – i.e. the risk
         that a single company’s stock may go down (i.e. ITC) This is frequently
         called idiosyncratic risk.
        Non-diversifiable – risk that is common to all investing in general and
         that cannot be reduced – i.e. the risk that the entire stock market (or
         bond market, or real estate market) will crash. This is frequently called
         systematic risk.
   The market “pays” you for bearing non-diversifiable risk only – not
    for bearing diversifiable risk.
        In general the more non-diversifiable risk that you bear, the greater the
         expected return to your investment(s).
        Many investors fail to properly diversify, and as a result bear more risk
         than they have to in order to earn a given level of expected return.

   In this sense, we can view the field of finance as being
    about two issues:
       The elimination of diversifiable risk in portfolios;
       The allocation of systematic (non-diversifiable) risk to those
        members of society that are most willing to bear it.

   Indeed, it is really this second function – the allocation
    of systematic risk – that drives rates of return.
       The expected rate of return is the “price” that the market pays
        investors for bearing systematic risk.

   A derivative (or derivative security) is a financial
    instrument whose value depends upon the value of
    other, more basic, underlying variables.

   Some common examples include things such as stock
    options, futures, and forwards.

   It can also extend to something like a reimbursement
    program for college credit. Consider that if your firm
    reimburses 100% of costs for an “A”, 75% of costs for
    a “B”, 50% for a “C” and 0% for anything less.

   Your “right” to claim this reimbursement, then is tied to
    the grade you earn. The value of that reimbursement
    plan, therefore, is derived from the grade you earn.

   We also say that the value is contingent upon the grade
    you earn. Thus, your claim for reimbursement is a
    “contingent” claim.

   The terms contingent claims and derivatives are used

   So why do we have derivatives and derivatives markets?
       Because they somehow allow investors to better control the
        level of risk that they bear.
       They can help eliminate idiosyncratic risk.
       They can decrease or increase the level of systematic risk.

                    A First Example
   There is a neat example from the bond-world of a
    derivative that is used to move non-diversifiable risk
    from one set of investors to another set that are,
    presumably, more willing to bear that risk.

   Disney wanted to open a theme park in Tokyo, but did
    not want to have the shareholders bear the risk of an
    earthquake destroying the park.
       They financed the park through the issuance of earthquake
       If an earthquake of at least 7.5 hit within 10 km of the park, the
        bonds did not have to be repaid, and there was a sliding scale
        for smaller quakes and for larger ones that were located further
        away from the park.

                    A First Example
   Normally this could have been handled in the insurance
    (and re-insurance) markets, but there would have been
    transaction costs involved. By placing the risk directly
    upon the bondholders Disney was able to avoid those
    transactions costs.
       Presumably the bondholders of the Disney bonds are basically
        the same investors that would have been holding the stock or
        bonds of the insurance/reinsurance companies.
       Although the risk of earthquake is not diversifiable to the park, it
        could be to Disney shareholders, so this does beg the question
        of why buy the insurance at all.
   This was not a “free” insurance. Disney paid LIBOR+310
    on the bond. If the earthquake provision was not it
    there, they would have paid a lower rate.

   Positions – In general if you are buying an asset – be it
    a physical stock or bond, or the right to determine
    whether or not you will acquire the asset in the future
    (such as through an option or futures contract) you are
    said to be “LONG” the instrument.
   If you are giving up the asset, or giving up the right to
    determine whether or not you will own the asset in the
    future, you are said to be “SHORT” the instrument.
       In the stock and bond markets, if you “short” an asset, it means
        that you borrow it, sell the asset, and then later buy it back.
       In derivatives markets you generally do not have to borrow the
        instrument – you can simply take a position (such as writing an
        option) that will require you to give up the asset or
        determination of ownership of the asset.
       Usually in derivatives markets the “short” is just the negative of
        the “long” position
   Commissions – Virtually all transactions in the financial
    markets requires some form of commission payment.
       The size of the commission depends upon the relative position of
        the trader: retail traders pay the most, institutional traders pay
        less, market makers pay the least (but still pay to the
       The larger the trade, the smaller the commission is in
        percentage terms.
   Bid-Ask spread – Depending upon whether you are
    buying or selling an instrument, you will get different
    prices. If you wish to sell, you will get a “BID” quote,
    and if you wish to buy you will get an “ASK” quote.

   The difference between the bid and the ask can vary
    depending upon whether you are a retail, institutional, or
    broker trader; it can also vary if you are placing very
    large trades.
   In general, however, the bid-ask spread is relatively
    constant for a given customer/position.
   The spread is roughly a constant percentage of the
    transaction, regardless of the scale – unlike the
   Especially in options trading, the bid-ask spread is a
    much bigger transaction cost than the commission.

   Here are some example stock bid-ask spreads from
            IBM:          Bid – 78.77   Ask – 78.79   0.025%
            ATT:          Bid – 30.59   Ask – 30.60   0.033%
            Microsoft:    Bid – 25.73   Ask – 25.74   0.039%
   Here are some example option bid-ask spreads (All with
    good volume)
       IBM Oct 85 Call:   Bid – 2.05    Ask – 2.20    7.3171%
       ATT Oct 15 Call:   Bid – 0.50    Ask –0.55     10.000%
       MSFT Oct 27.5 :    Bid – 0.70    Ask –0.80.    14.285%

   The point of the preceding slide is to demonstrate that
    the bid-ask spread can be a huge factor in determining
    the profitability of a trade.
       Many of those option positions require at least a 10% price
        movement before the trade is profitable.
   Many “trading strategies” that you see people propose
    (and that are frequently demonstrated using “real” data)
    are based upon using the average of the bid-ask spread.
    They usually lose their effectiveness when the bid-ask
    spread is considered.

   Market Efficiency – We normally talk about financial markets as
    being efficient information processors.
        Markets efficiently incorporate all publicly available information into
         financial asset prices.
        The mechanism through which this is done is by investors
         buying/selling based upon their discovery and analysis of new
        The limiting factor in this is the transaction costs associated with the
        For this reason, it is better to say that financial markets are efficient to
         within transactions costs. Some financial economists say that
         financial markets are efficient to within the bid-ask spread.
        Now, to a large degree for this class we can ignore the bid-ask spread,
         but there are some points where it will be particularly relevant, and we
         will consider it then.

   Before we begin to examine specific contracts, we need
    to consider two additional risks in the market:
       Credit risk – the risk that your trading partner might not honor
        their obligations.
            Familiar risk to anybody that has traded on ebay!
            Generally exchanges serve to mitigate this risk.
            Can also be mitigated by escrow accounts.
                  Margin requirements are a form of escrow account.
       Liquidity risk – the risk that when you need to buy or sell an
        instrument you may not be able to find a counterparty.
            Can be very common for “outsiders” in commodities markets.

   So now we are going to begin examining the basic
    instruments of derivatives. In particular we will look at
       Forwards
       Futures
       Options
   The purpose of our discussion is to simply provide a
    basic understanding of the structure of the instruments
    and the basic reasons they might exist.

                Forward Contracts
A forward contract is an agreement between two parties to
    buy or sell an asset at a certain future time for a certain
    future price.
      Forward contracts are normally not exchange traded.
      The party that agrees to buy the asset in the future is said to
       have the long position.
      The party that agrees to sell the asset in the future is said to
       have the short position.
      The specified future date for the exchange is known as the
       delivery (maturity) date.

               Forward Contracts
The specified price for the sale is known as the delivery
   price, we will denote this as K.
      Note that K is set such that at initiation of the contract the value
       of the forward contract is 0. Thus, by design, no cash changes
       hands at time 0. The mechanics of how to do this we cover in
       later lectures.
As time progresses the delivery price doesn’t change, but
   the current spot (market) rate does. Thus, the contract
   gains (or loses) value over time.
      Consider the situation at the maturity date of the contract. If
       the spot price is higher than the delivery price, the long party
       can buy at K and immediately sell at the spot price ST, making a
       profit of (ST-K), whereas the short position could have sold the
       asset for ST, but is obligated to sell for K, earning a profit
       (negative) of (K-ST).

                Forward Contracts
   Example:
       Let’s say that you entered into a forward contract to buy wheat
        at $4.00/bushel, with delivery in December (thus K=$3.64.)
       Let’s say that the delivery date was December 14 and that on
        December 14th the market price of wheat is unlikely to be
        exactly $4.00/bushel, but that is the price at which you have
        agreed (via the forward contract) to buy your wheat.
       If the market price is greater than $4.00/bushel, you are
        pleased, because you are able to buy an asset for less than its
        market price.
       If, however, the market price is less than $4.00/bushel, you are
        not pleased because you are paying more than the market price
        for the wheat.
       Indeed, we can determine your net payoff to the trade by
        applying the formula: payoff = ST – K, since you gain an asset
        worth ST, but you have to pay $K for it.
       We can graph the payoff function:
                              Forward Contracts
                                     Payoff to Futures Position on Wheat
                                  Where the Delivery Price (K) is $4.00/Bushel



Payoff to Forwards


                          0   1        2           3         4         5            6   7   8



                                           Wheat Market (Spot) Price, December 14

                Forward Contracts
   Example:
       In this example you were the long party, but what about the
        short party?
       They have agreed to sell wheat to you for $4.00/bushel on
        December 14.
       Their payoff is positive if the market price of wheat is less than
        $4.00/bushel – they force you to pay more for the wheat than
        they could sell it for on the open market.
           Indeed, you could assume that what they do is buy it on the open
            market and then immediately deliver it to you in the forward
       Their payoff is negative, however, if the market price of wheat is
        greater than $4.00/bushel.
           They could have sold the wheat for more than $4.00/bushel had
            they not agreed to sell it to you.
       So their payoff function is the mirror image of your payoff
                                  Forward Contracts
                                   Payoff to Short Futures Position on Wheat
                                  Where the Delivery Price (K) is $4.00/Bushel



Payoff to Forwards


                          0   1        2           3         4         5            6   7   8



                                           Wheat Market (Spot) Price, December 14

               Forward Contracts
   Clearly the short position is just the mirror image of the
    long position, and, taken together the two positions
    cancel each other out:

                             Forward Contracts
                             Long and Short Positions in a Forward Contract
                                       For Wheat at $4.00/Bushel


                                         Short Position

                                                                              Long Position

              0          1         2         3        4        5        6          7          8

                                                 Wheat Price

                 Futures Contracts
   A futures contract is similar to a forward contract in that it
    is an agreement between two parties to buy or sell an
    asset at a certain time for a certain price. Futures,
    however, are usually exchange traded and, to facilitate
    trading, are usually standardized contracts. This results in
    more institutional detail than is the case with forwards.

   The long and short party usually do not deal with each
    other directly or even know each other for that matter.
    The exchange acts as a clearinghouse. As far as the two
    sides are concerned they are entering into contracts with
    the exchange. In fact, the exchange guarantees
    performance of the contract regardless of whether the
    other party fails.
                Futures Contracts
   The largest futures exchanges are the Chicago Board of
    Trade (CBOT) and the Chicago Mercantile Exchange

   Futures are traded on a wide range of commodities and
    financial assets.

   Usually an exact delivery date is not specified, but rather
    a delivery range is specified. The short position has the
    option to choose when delivery is made. This is done to
    accommodate physical delivery issues.
       Harvest dates vary from year to year, transportation schedules
        change, etc.

                 Futures Contracts
   The exchange will usually place restrictions and conditions
    on futures. These include:
       Daily price (change) limits.
       For commodities, grade requirements.
       Delivery method and place.
       How the contract is quoted.

   Note however, that the basic payoffs are the same as for a
    forward contract.

                 Options Contracts
   Options on stocks were first traded in 1973. That was
    the year the famous Black-Scholes formula was
    published, along with Merton’s paper - a set of
    academic papers that literally started an industry.
   Options exist on virtually anything. Tonight we are
    going to focus on general options terminology for
    stocks. We will get into other types of options later in
    the class.
   There are two basic types of options:
       A Call option is the right, but not the obligation, to buy the
        underlying asset by a certain date for a certain price.
       A Put option is the right, but not the obligation, to sell the
        underlying asset by a certain date for a certain price.
           Note that unlike a forward or futures contract, the holder of the
            options contract does not have to do anything - they have the
            option to do it or not.

                 Options Contracts
   The date when the option expires is known as the
    exercise date, the expiration date, or the maturity date.
   The price at which the asset can be purchased or sold is
    known as the strike price.
   If an option is said to be European, it means that the
    holder of the option can buy or sell (depending on if it is
    a call or a put) only on the maturity date. If the option is
    said to be an American style option, the holder can
    exercise on any date up to and including the exercise
   An options contract is always costly to enter as the long
    party. The short party always is always paid to enter into
    the contract
       Looking at the payoff diagrams you can see why…

                   Options Contracts
   Let’s say that you entered into a call option on IBM
       Today IBM is selling for roughly $78.80/share, so let’s say you
        entered into a call option that would let you buy IBM stock in
        December at a price of $80/share.
       If in December the market price of IBM were greater than $80,
        you would exercise your option, and purchase the IBM share for
       If, in December IBM stock were selling for less than $80/share,
        you could buy the stock for less by buying it in the open market,
        so you would not exercise your option.
                Thus your payoff to the option is $0 if the IBM stock is less than $80
                It is (ST-K) if IBM stock is worth more than $80
       Thus, your payoff diagram is:

                        Options Contracts
                                   Long Call on IBM
                               with Strike Price (K) = $80





               0   20     40      60        K =80        100      120   140   160
                                       IBM Terminal Stock Price


                Options Contracts
   What if you had the short position?
   Well, after you enter into the contract, you have granted the
    option to the long-party.
   If they want to exercise the option, you have to do so.
   Of course, they will only exercise the option when it is in there
    best interest to do so – that is, when the strike price is lower
    than the market price of the stock.
        So if the stock price is less than the strike price (ST<K), then the
         long party will just buy the stock in the market, and so the option
         will expire, and you will receive $0 at maturity.
        If the stock price is more than the strike price (ST>K), however,
         then the long party will exercise their option and you will have to
         sell them an asset that is worth ST for $K.
   We can thus write your payoff as:
             payoff = min(0,ST-K),
     which has a graph that looks like:

                                        Options Contracts
                                              Short Call Position on IBM Stock
                                                 with Strike Price (K) = $80


Payoff to Short Position

                                    0   20   40      60        80        100     120   140   160




                                                          Ending Stock Price

                 Options Contracts
   This is obviously the mirror image of the long position.
   Notice, however, that at maturity, the short option
    position can NEVER have a positive payout – the best
    that can happen is that they get $0.
       This is why the short option party always demands an up-front
        payment – it’s the only payment they are going to receive. This
        payment is called the option premium or price.

   Once again, the two positions “net out” to zero:

                       Options Contracts
                          Long and Short Call Options on IBM
                               with Strike Prices of $80

          40                                  Long Call
                  Net Position

          -20 0   20      40      60        80       100    120   140   160

                                            Short Call
                                       Ending Stock Price

               Options Contracts
   Recall that a put option grants the long party the right to
    sell the underlying at price K.
   Returning to our IBM example, if K=80, the long party
    will only elect to exercise the option if the price of the
    stock in the market is less than $80, otherwise they
    would just sell it in the market.
   The payoff to the holder of the long put position,
    therefore is simply
                payoff = max(0, K-ST)

                      Options Contracts
                             Payoff to Long Put Option on IBM
                                  with Strike Price of $80


         -10 0   20     40         60        80        100      120   140   160

                                        Ending Stock Price

               Options Contracts
   The short position again has granted the option to the
    long position. The short has to buy the stock at price K,
    when the long party wants them to do so. Of course the
    long party will only do this when the stock price is less
    than the strike price.
   Thus, the payoff function for the short put position is:
        payoff = min(0, ST-K)

   And the payoff diagram looks like:

                      Options Contracts
                                Short Put Option on IBM
                                 with Strike Price of $80

                  0   20   40       60        80        100   120   140   160




                                         Ending Stock Price

               Options Contracts
   Since the short put party can never receive a positive
    payout at maturity, they demand a payment up-front
    from the long party – that is, they demand that the long
    party pay a premium to induce them to enter into the

   Once again, the short and long positions net out to zero:
    when one party wins, the other loses.

                       Options Contracts
                         Long and Short Put Options on IBM
                              with Strike Prices of $80

          60                  Long Position
                                                       Net Position

          -20 0   20     40       60        80        100     120     140   160
          -60                 Short Position
                                       Ending Stock Price

                 Options Contracts
   The standard options contract is for 100 units of the
    underlying. Thus if the option is selling for $5, you
    would have to enter into a contract for 100 of the
    underlying stock, and thus the cost of entering would
    be $500.
   For a European call, the payoff to the option is:
                       Max(0,ST-K)
   For a European put it is
                       Max(0,K-ST)
   The short positions are just the negative of these:
       Short call: -Max(0,ST-K) = Min(0,K-ST)
       Short put: -Max(0,K-ST) = Min(0,ST-K)

                   Options Contracts
   Traders frequently refer to an option as being “in the
    money”, “out of the money” or “at the money”.
       An “in the money” option means one where the price of the
        underlying is such that if the option were exercised immediately,
        the option holder would receive a payout.
            For a call option this means that St>K
            For a put option this means that St<K
       An “at the money” option means one where the strike and
        exercise prices are the same.
       An “out of the money” option means one where the price of the
        underlying is such that if the option were exercised immediately,
        the option holder would NOT receive a payout.
            For a call option this means that St<K
            For a put option this means that St>K.

                          Options Contracts
                                      Long Call on IBM
                                  with Strike Price (K) = $80



                                               At the money

                   Out of the money                                    In the money

               0     20      40       60       K = 80        100      120    140      160
                                           IBM Terminal Stock Price


               Options Contracts
   One interesting notion is to look at the payoff from just
    owning the stock – its value is simply the value of the

                         Options Contracts
                        Payout Diagram for a Long Position in IBM Stock










               0   20         40      60        80        100   120       140   160
                                           Ending Stock Price

               Options Contracts
   What is interesting is if we compare the payout from a
    portfolio containing a short put and a long call with the
    payout from just owning the stock:

                    Options Contracts
                         Payout Diagram for a Long Position in IBM Stock


                                                                     Long Call


                0   20         40        60          80       100    120         140   160
                                    Short Put

                                                Ending Stock Price

               Options Contracts
   Notice how the payoff to the options portfolio has the
    same shape and slope as the stock position – just offset
    by some amount?

   This is hinting at one of the most important relationships
    in options theory – Put-Call parity.

   It may be easier to see this if we examine the aggregate
    position of the options portfolio:

                    Options Contracts
                    Payout Diagram for a Long Position in IBM Stock





                0   20     40      60        80       100    120      140   160

                                        Ending Stock Price

                  Options Contracts
   We will come back to put-call parity in a few weeks, but
    it is well worth keeping this diagram in mind.

   So who trades options contracts? Generally there are
    three types of options traders:
       Hedgers - these are firms that face a business risk. They wish
        to get rid of this uncertainty using a derivative. For example, an
        airline might use a derivatives contract to hedge the risk that jet
        fuel prices might change.
       Speculators - They want to take a bet (position) in the market
        and simply want to be in place to capture expected up or down
       Arbitrageurs - They are looking for imperfections in the capital


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