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Computational Finance Lecture 4 Futures and Swaps


									Computational Finance

       Lecture 4
         Part II
   Futures and Swaps
                    Main Contents
n       Futures contracts
    n   Trading Mechanism: clearinghouse and margins
    n   Using Futures to Hedge
    n   Financial Futures
n       Swaps
    n   Swaps Basics
    n   Swaps and Balance Sheet Restructing
    n   Pricing
4.3 Futures Contracts
n   The trading of forward contracts is usually over-
    the-counter. It involves risks. Sometimes one of
    the parties may not have enough financial
    resources, or may regret the deal, to honor the
n   To avoid the risk, futures (期貨) contracts are
    n   Standardized contract terms such as delivery dates,
        price units, contract size
    n   Traded on an exchange
                  Futures Exchanges
n   Exchanges in the world:
    n   US: The Chicago Board of Trade (CBOT) and the
        Chicago Mercantile Exchange (CME) used to be the two
        largest futures exchanges in the US. In 2007, the CBOT
        and the CME merged to form the CME Group
    n   Europe: Eurex, jointly owned by the Deutsche Borse
        and Swiss exchange, is currently the world’s largest
        futures exchange.
    n   China: Shanghai Futures, Dalian Commodity,
        Zhengzhou Commodity.
    The Clearinghouse and Open Interest

n   Exchanges play a role of clearinghouse, acting as
    the other party to all buyers and sellers. It is
    obligated to deliver the commodity to the long
    position and to pay for delivery from the short at
    contract maturity.
    The Clearinghouse and Open Interest

n   The clearinghouse makes it possible for traders to
    liquidate position easily. If you are currently long
    in a contract and want to undo your position, you
    simply instruct your broker to enter the short side
    of a contract to close out your position. This is
    called a reversing trade.
n   Most trades are reversed before the maturity and
    do not result in actual delivery.
n   The open interest on a contract is the number of
    contracts outstanding.
        Specification of Futures Contract
n   When developing a new contract, the exchange
    must specify in detail the exact nature of the
    agreement between the two parties.
    n   The asset quality and the contract size
    n   Delivery arrangement and months
    n   Price limits and position limits
       Marking to Market and Margins
n   One of the key roles of the exchange is to organize
    trading so that contract defaults can be avoided
    effectively. In practice, trading on margin is
    introduced to ensure this.
n   At initial execution of a trade, traders establish a
    margin account. The margin is a security account
    consisting of cash or near-cash securities, such as
    Treasury bills, that ensures the trader will be able
    to satisfy the obligation of the futures contract.
       The Operation of Margins:
    Margin Account and Initial Margins
n   An investor wants to buy two March gold futures
    contracts on the New York Commodity Exchange.
n   Each contract size is 100 ounces. The current
    futures price is $600 per ounce and the initial
    margin is $2,000 per contract.
n   Investor should deposit $4,000 in his margin
            The Operation of Margins:
               Marking to Market
n   On any day that futures contract trade, the
    clearinghouse requires all positions to recognize
    profits as they accrue daily.
    n   For instance, on the next day, the March gold futures
        price drops down to $597 per ounce. The investor has a
        loss of
        2   ($600-$597) 100 =$600.
    n   $600 is deducted from the margin of the investor and
        the total balance is reduced to $4,000-$600=$3,400.
          The Operation of Margins:
             Marking to Market
  n   Similarly, the March gold futures price climbs up to
      $599 per ounce on the third day. The investor gains
      2   ($599-$597) 100 =$400.
  n   $400 is added to the margin of the investor and the total
      balance is reduced to $3,400+$400=$3,800.
           The Operation of Margins:
             Maintenance Margin
n   Usually the exchanges will set a lower bound for
    each margin account, known as the maintenance
    margin to prevent the balance in the margin
    account from being negative.
n   Once the balance is below the maintenance
    margin, the investor will receive a margin call to
    top up the account to the initial level. The extra
    funds deposited are known as variation margin.
    If the investor fails to do so, the broker close out
    the position.
n   If a futures contract is not closed out before
    maturity, it is usually settled by delivering the
    assets underlying the contract.
n   The short position issues a notice of intention to
    the exchange to state how many contracts will be
    delivered and also specifies where to deliver and
    what grade will be delivered. The exchange
    chooses a party with a long position to accept
n   A few futures are settled in cash.
Forward Contracts vs Futures Contracts

          FORWARDS                           FUTURES
Private contract between 2 parties         Exchange traded

     Non-standard contract                Standard contract

 Usually 1 specified delivery date      Range of delivery dates

       Settled at end of contract            Settled daily

      Delivery or final cash         Contract usually closed out
     settlement usually occurs            prior to maturity
          Some credit risk               Virtually no credit risk
          Forward vs Futures Prices
n   Forward and futures prices are usually assumed
    to be the same. Therefore, we may use forward
    price as a good approximation to price futures.
n   When interest rates are uncertain, in theory, these
    two prices are slightly different:
    n A strong positive correlation between interest rates and
      the asset price implies the futures price is slightly
      higher than the forward price
    n A strong negative correlation implies the reverse

    (See Appendix in Chapter 5 of John Hull)
4.4 Hedging Strategies Using
     Futures Contracts
         Hedging Strategies in Futures
n   Speculation
    n   Go short if you believe price will fall
    n   Go long if you believe price will rise
n   Hedge
    n   Long hedge
    n   Short hedge
                          Short Hedge
n   A short hedge is a hedge that involves a short
    position in futures contract. It is appropriate when
    you know you will sell an asset in the future and
    want to lock in the price.
    n   Assume an oil producer has just negotiated a contract to sell 1
        million barrels of crude oil on Feb 20, 2013. It has been agreed
        that the price that will apply in the contract is the market price on
        that day.
    n   The producer may short 1,000 3-month futures contract with
        1,000 barrels each. Suppose that the futures price is $59 per barrel
        on the New York Mercantile Exchange (NYMEX). The producer
        can lock in the price at $59 per barrel on Feb 20.
                         Long Hedge
n   A short hedge is a hedge that involves a long
    position in futures contract. It is an appropriate
    instrument when you know you will buy an asset
    in the future and want to lock in the price.
    n   Assume a copper fabricator knows it will require 100,000 pounds
        of copper on Feb 20, 2013 to meet a certain contract.
    n   The fabricator can hedge its position by longing futures contracts
        with 100,000 pounds. The futures price for Feb delivery is 320
        cents per pound. The strategy has an effect of locking in the price
        of the required copper at close to 320 cents per pound.
4.5 Financial Futures
                  Financial Futures
n   Although futures markets have their origin in
    agriculture commodities, today’s market is
    dominated by contracts on financial assets.
    n   Stock index futures
    n   Foreign exchange futures
    n   Interest-rate futures
Stock Index Futures and Cash Settlement
n   Futures trade actively on stock market indexes.
    These contracts are settled by a cash amount
    equal to the value of the stock index in question
    on contract maturity date times a multiplier that
    scales the size of the contract.
n   This cash settlement duplicates the profits/losses
    that would arise with actual delivery.
Stock Index Futures in Major Exchanges
     Creating Synthetic Stock Position
n   One reason of the popularity of stock index
    futures is that they can let investors participate in
    broad market movements without actually buying
    or selling large numbers of stocks.
    n   Allows frequent trading at low cost.
n   Strategies:
    n   Market timing by switching between Treasury bills
        and stock index futures
    n   Index arbitrage and program trading
4.6 Swaps
n   A swap (掉期) is an agreement to exchange cash
    flows at specified future times according to certain
    specified rules.
n   A forward contract can be viewed as a simple
    example of a swap. Swaps are multi-period
    extension of forward contracts.
    n   A company enters into a forward contract to buy 100
        ounces of gold for $900 per ounce in one year. It is
        equivalent to a swap where the company agrees it will
        use $90,000 to exchange for 100 ounces of gold.

n   The swap market is a large component of
    derivatives market, with well over US$200 trillion
    n   Interest rate swaps
         n   One party agrees to pay the counterparty a fixed rate of interest
             in exchange for paying a variable/floating rate of interest or
             vice versa
    n   Foreign exchange swaps
         n   An exchange of currencies on several future dates
    An Example of Interest Rate Swap
n   An agreement by Microsoft to receive 6-month
    LIBOR from Intel and to pay Intel a fixed rate
    of 5% per annum every 6 months for 3 years on
    a notional principal of $100 million.
n   LIBOR, the London Interbank Offered Rate, is a
    kind of interest rates at which a bank is prepared
    to deposit money with other banks in the
    Eurocurrency market. Typically, 1-month, 3-
    month, 6-month, and 12-month LIBOR rates are
    quoted in all major currencies.
n   It is calculated by British Bankers’ Association
    (BBA) and released to the market shortly after
    11am London time every day.
 Cash Flows of Interest Rate Swaps

                       ---------Millions of Dollars---------
                LIBOR FLOATING FIXED                  Net
   Date         Rate   Cash Flow Cash Flow Cash Flow
Nov. 20, 2012   4.2%
May 20, 2013    4.8%     +2.10        –2.50         –0.40
Nov. 20, 2013   5.3%     +2.40        –2.50         –0.10
May 20, 2014    5.5%     +2.65        –2.50         +0.15
Nov. 20, 2014   5.6%     +2.75        –2.50         +0.25
May. 20, 2015 5.9%       +2.80        –2.50         +0.30
Nov. 20, 2015   6.4%     +2.95        –2.50         +0.45
             Uses of Interest Rate Swaps
n   Converting a liability from
    n    a floating rate to a fixed rate
         In the previous example, suppose that Microsoft has arranged to borrow
         $100 million at LIBOR + 0.1%. But it wishes to pay at a fixed rate.
    n    a fixed rate to floating rate
         Intel, has a 3-year $100 million loan outstanding with a fixed rate 5.2%
         and it wants to pay at a floating rate.
          Uses of Interest Rate Swaps
n   Before a swap:

5.2%        Intel            MicroSoft

                                         LIBOR +0.1%

    n   Intel pays 5.2%;
    n   Microsoft pays LIBOR+0.1%.
          Uses of Interest Rate Swaps
n   After a swap:

5.2%         Intel            MicroSoft

                      LIBOR               LIBOR +0.1%

    n   Intel pays LIBOR + 0.2%;
    n   Microsoft pays 5.1%.
             Uses of Interest Rate Swaps
n   Converting an asset from
    n    a fixed rate to a floating rate
         In the previous example, suppose that Microsoft owns $100 million in a
         bond that will provide interest at 4.7%. And it wishes to earn a floating
    n    a floating rate to a fixed rate
         Intel has an investment of $100 million that yields LIBOR-0.2% and it
         wants a fixed rate.
             Uses of Interest Rate Swaps
n   Before a swap:

LIBOR-0.2%    Intel               MicroSoft

    n   Intel earns LIBOR-0.2%;
    n   Microsoft earns 4.7%.
             Uses of Interest Rate Swaps
n   After a swap:
                      5%                   4.7%

LIBOR-0.2%    Intel            MicroSoft


    n   Intel earns 4.8%;
    n   Microsoft earns LIBOR-0.3%.
Swaps and Balance Sheet Restructuring
n   The previous example illustrates why interest rate
    swaps have tremendous appeal to fixed-income
    managers. These contracts provide a means to
    quickly, cheaply, and anonymously restructure the
    balance sheet.
        Role of Financial Intermediary
n   Usually two nonfinancial companies do not get in
    touch directly to arrange a swap. They each deal
    with a financial intermediary to swap their cash
        Role of Financial Intermediary
n   Illustration:

                4.985%                     5.015%
5.2%                          Financial                         LIBOR
        Intel                                       Microsoft
                            Intermediary                        +0.1%
                    LIBOR                  LIBOR
4.7 Valuation of Swaps
      Valuation of an Interest Rate Swap
n   Interest rate swaps can be valued as the
    difference between the value of a fixed-rate bond
    and the value of a floating-rate bond.
n   Alternatively, they can be valued as a portfolio
    of forwards.
n   Contract terms: pay 6-month LIBOR, receive 8%
    per annum on a principal of $100 million.
n   The contract has a remaining life of 1.25 years and
    the last payment date was 3 month ago.
n   LIBOR rates for 3-months, 9-months and 15-
    months are 10%, 10.5%, and 11%. The 6-month
    LIBOR on last payment date was 10.2%.
n   Cash flow analysis:


    0      0.25        0.75    1.25

          4M      4M    104M
                Valuation Using Bonds

Time Bfix cash    Bfl cash   Discout PV        PV
     flow         flow       factor  Bfix      Bfl
0.25    4.0       105.100    0.9753   3.901    102.505
0.75    4.0                  0.9243   3.697
1.25    104.0                0.8715   90.640
Total                                 98.238   102.505
         Valuation Using Forward Rates

Time    Fixed   Floating Net      Disc     PV
        cash    cash     Cash     factor   Bfl
        flow    flow     Flow
0.25    4.0     -5.100   -1.100   0.9753   -1.073
0.75    4.0     -5.522   -1.522   0.9243   -1.407
1.25    4.0     -6.051   -2.051   0.8715   -1.787
Total                                      -4.267
                  Currency Swaps

n   Another popular type of swaps is known as
    currency swaps.
n   A currency swap requires the principal to be
    specified in each of the two currencies. Two
    parties exchange the principals at the beginning
    and end of the life of the swap.
n   An agreement to pay 5% on a GBP principal of
    £10 million & receive 6% on a US$ principal of
    $18 million every year for 5 years.
n   Associated cash flows
                    Dollars      Pounds
             Year     ------millions------
             2012   –18.00       +10.00
             2013    +1.08        –0.50

                     +1.08        –0.50
            2015     +1.08         –0.50
             2016    +1.08         -0.50
                    +19.08        −10.50
    Use of a Currency Swap to Transform
            Liabilities and Assets
n   A currency swap can be used to transform
    borrowings/investments in one currency to
    borrowing/investments in another.
         Valuation of Currency Swaps
n   Like interest rate swaps, currency swaps can be
    valued either as the difference between 2 bonds or
    as a portfolio of forward contracts
n   Suppose that the term structures of interest rates in
    both Japan and the US are flat. The Jap rate is 4%
    per year and the US rate is 9% per year.
n   A currency swap was entered into some time ago.
    The financial institution receives 5% per year in
    yen and pays 8% per year in USD. The principals
    are US$10 million and 1,200 million yen. The
    contract will last for another 3 years.
n   The current exchange rate is 110 yen per dollar.
          Valuation in Terms of Bonds

Time     Cash Flows   PV       Cash flows   PV (yen)
         ($)          ($)      (yen)
  1          0.8      0.7311        60        57.65
  2          0.8      0.6682        60        55.39
  3          0.8      0.6107        60        53.22
  3          10.0     7.6338       1,200     1,064.30
 Total                9.6439                 1,230.55
          Valuation in Terms of Forwards

Time $ cash     Yen      Forward Yen cash Net           Presen
     flow       cash     Exch    flow in $ Cash         t value
                flow     rate              Flow
 1      -0.8       60    0.009557   0.5734    -0.2266    -0.2071
 2      -0.8       60    0.010047   0.6028    -0.1972    -0.1647
 3      -0.8       60    0.010562   0.6337    -0.1663    -0.1269
 3      -10.0     1200   0.010562   12.6746   +2.6746    2.0417
Total                                                    1.5430

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