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					Derivatives

  Chapter 9
             Spot vs. Derivative
• Spot Markets: Asset market in which immediate
  transfer of asset or cash is made.
• Derivative Market: Market in which transactors
  agree to transfer assets at some prespecified price
  at some future date.
   –   Forwards
   –   Futures
   –   Swaps
   –   Options
        Forwards and Futures
• Forward Contract: Agreement to exchange
  some asset at prespecified date and price.
  Forwards are non-standardized and are
  agreed upon on a case by case basis by
  traders (Over the Counter Market).
• Futures Contract: Agreement to exchange
  some asset at prespecified date and price.
  Contracts are standardized and offered by
  exchanges.
          Timeline of a Future
                            Settlement Date




Buyer or Seller          Seller delivers
Contracts a Settlement   underlying asset to the
Price with Exchange.     exchange or exchange
                         delivers underlying
                         asset to buyer.
               Long vs. Short
• The counter-party to a future will be a member of
  the exchange.
• Long position: Investor buys a future.
• Short position: Investor sells a future.
• Conceptually, buying an interest future is like
  promising to make a deposit at the future interest
  rate and selling a future is like making a promise
  to take a deposit at the purchase interest rate.
               Interest Rate Futures
• For a stock future, a seller contracts to deliver shares in
  the stock to the exchange on the settlement date while a
  buyer will have shares delivered to them.
• For a wheat future, a seller contracts to deliver bushels
  of wheat to the exchange while a buyer will have wheat
  delivered to them.
• For interest rate futures, a seller contracts to deliver a
  bank account with a predetermined interest rate to the
  exchange on the settlement date while a buyer will have
  a bank account to them.
        Interest Rate Futures
• Q: How do you deliver a bank account?
• A: In reality, its impossible to deliver a
  bank account. Instead, the exchange and the
  investor will agree to make a payment
  which will be equivalent to the net value of
  a bank account with a preset rate delivered
  on the day of the settlement.
       HK Clearing and Exchange
                                                Average Daily Volume
                           Link: October 2006   # of Contracts

•  HK EX monopolizes       Stock Index
   trading of futures
   contracts and this is   Futures                           77,757
   overwhelmingly an       Individual Stock
   equity market.          Futures                                 446
• Three Interest Rate
   Derivative Products
1. One-Month HIBOR         Index Options                      20592
   Futures                 Individual Stock
2. Three-Month HIBOR       Options                           71,704
   Futures
3. Three-Year Exchange     Interest Rate
   Fund Note (EFN)         Futures                                     48
     Chicago Mercantile Exchange
      International Money Market
• Pioneer of the Interest Rate Derivative products
  and still the largest market for interest rate futures.
• Largest Product: 3 Month (90 days or ¼ of a
  year) Eurodollar Futures (average daily trading
  volume, about 2.2 million contracts per day).
  Contract Specification
• What is a Eurodollar? A time deposit at a bank
  outside the USA denominated in US dollars.
                Interest Rate Future
• Conceptually, an interest rate future is an entitlement
  to deposit money into a bank account at some pre-
  specified interest rate.
• Example: Merc Eurodollar Future is a theoretical
  entitlement to deposit US$1Million at some future
  date (buyers have a choice of settlement dates at any
  End of Quarter for next 10 years, 40 choices).
Menu of Choices
• Price of the contract determines the interest rate.
Future Rate (in annualized % terms)
  = 100 – Settlement Price Flash Quote
                 Replicate Value
• Example: On November 20, 2006, a 3 month
  Eurodollar future with a settlement date of September
  30, 2007 was priced at PRICE = 95.08 corresponding to
  a Purchase interest rate of 4.92% (i=.0492).
• If an investor buys this future than the exchange will
  have to pay the investor the net value of a 3 month bank
  deposit made on the settlement date (30-9-07) that
  offers the purchase interest rate (4.92%).
• How much is that value? Answer depends on the
  prevailing interest rates on 3 month time deposits of
  cash on the actual settlement date.
                Example (Cont.)
• What if the prevailing cash interest rate on 3 month
  Eurodollars at September 30, 2007 was 3%.
• A cash deposit 3% would earn interest over ¼ of a
  year. .03 
           i
                   1
                   4     $1Million  $7,500
                Fraction of Year       Principal



• A (hypothetical) deposit at 4.92% would earn
         .0492            1
                           4            $1Million  $12,300
            i       Fraction of Year         Principal


• Net Value of a Bank Deposit at 4.92% is $12,300-
  $7500 = $4,800
     Replicating the Value of Making a
               Bank Deposit
• In general, Net Value of Making Bank Deposit at a
  pre-determined interest rate is:
Net Value =
  ( Future Rate at Purchase – Cash Interest Rate)
  * (# of Years of Underlying Instrument)
  * Principal
• Futures Exchange replicates the value of a making a
  bank deposit by paying a buyer of an interest rate
  future this net value.
     Replicating the Value of Taking a
               Bank Deposit
• In general, Net Value of Taking Bank Deposit at a
  pre-determined interest rate is:
Net Value =
  (Cash Interest Rate – Future Rate at Purchase)
  * (# of Years of Underlying Instrument)
  * Principal
• Futures Exchange replicates the value of a taking a
  bank deposit by paying a seller of an interest rate
  future this net value.
• What if cash interest rates rise?
• Example: If 3-month Eurodollar rate goes to
  7%, then value of making a deposit is
  (.0492-.07)*.25*$1million = -$5,200.
  – A buyer would have to pay the exchange $5200.
• Example: If 3month Eurodollar rate goes to 7%,
  then value of taking a deposit is
  (.07 -.0492 )* .25 * $1million = $5,200.
  – The exchange would have to pay a seller $5200.
              Structure of Payments
• The hypothetical value of the future changes every day
  as the settlement price changes and the accompanying
  future rate changes.
• For example, on November 21, 2006, the price of the
  Sep-07 3mo Eurodollar future falls to 95.07 (see Daily
  Update). The corresponding interest rate rises to 4.93%.

• Daily margin payments are made between the investor
  and the exchange which reflect these changes in value.
     Margin payment made by a buyer
• Margin payment made by a buyer to the exchange on a
  day to day basis.
Margin Payment =
(Market Future Ratetoday – Market Future Rateyesterday)
  * (# of Years of Underlying Instrument)*Principal
• If the future rate rises (or, equivalently, the settlement
  price falls) in a given day, someone who has bought an
  interest future in the past must make a payment to the
  exchange. When the interest rate falls, someone who has
  bought an interest rate future gets a payment from the
  exchange.
      Margin payment made by a seller
• Margin payment made by a buyer to the exchange on a
  day to day basis.
Margin Payment =
(Market Future Rateyesterday – Market Future Ratetoday)
  * (# of Years of Underlying Instrument) * Principal
• If the future rate falls (or, equivalently, the settlement
  price falls) in a given day, someone who has sold an
  interest future must make a payment to the exchange.
  When the interest rate rises, someone who has sold an
  interest rate future gets a payment from the exchange.
                              Final Value
• On the actual settlement day, T, the value of the
  future will be equal to the value of the underlying
  instrument (since you are contracting to deliver
  something that day). Future RateT = Cash RateT
• Sum of the daily changes in the future rate between
  the date of the initial purchase (time 0) and final
  settlement date is equal to the difference in the
  initial future rate and the future rate on the
  settlement date.
   (i1F  i0F )  (i2  i1F )  (i3F  i2 )  ....  (iT 1  iT 2 )  (iT  iT 1 )
                    F                   F              F       F          F    F


    (iT  i0F )  (iT
       F             CASH
                           i0F )
        Speculation vs. Hedging
•   Investors or financial institutions can buy futures
    as a speculative investment which allows some
    possibility of profit with some risk.
•   Futures may also be hedges: investments which
    will pay positive profits at the same time that the
    owner takes losses on some other assets. This
    offset allows the investor to reduce overall risk.
•   Banks do 2 types of hedging
    1. Microhedging: Hedge individual parts of the portfolio
    2. Macrohedging: Hedge aggregate risk of the portfolio
          Microhedge Example
• Problem: On January 1st, bank has an opportunity
  to make a $1,000,000, 6 month loan at a 5%
  interest rate. The bank can take a 3 month time
  deposit today at 3%.
• Lending at this spread is profitable, but bank
  worries that if interest rates rise unexpectedly over
  the course of the next 3 months, then they might
  take losses.
• Solution: Bank can make the loan. Accept cash
  deposits and simultaneously sell interest rate
  futures to the exchange.
           Example (cont.) Unhedged
• If the bank lends $1 mil. for half a year at a 5% interest rate,
  they will earn .05 * ½ * $1M = $2500 in interest income.
• For the first time deposit, they will pay 3% interest for a
  quarter of a year implying .03* ¼ * $1M = $750 in interest
  expenses for the 1st quarter.
• If the interest on time deposits is still 3% on March-31, 2007
  then they can renew their deposit and pay .03 * ¼ * $1M =
  $750 for the 2nd quarter implying total interest expenses of
  $750 + $750 = $1500 implying net interest income = $1000.
• If the interest rate on time deposits has risen to 7% on 3-31-
  07, then they can renew their deposit and pay .07 * ¼ * $1M
  = $1750 for the 2nd quarter implying total interest expenses
  of $750 + $1750 = $2500 implying net interest income = $0.
                      Hedging
• Lets say that a 3 month Eurodollar future with a
  settlement date of March 31, 2007 has a settlement
  price on January 1st, 2007 of 97 implying a future rate
  of 3%. At the same time that the bank makes the loan,
  they sell 1 future to the exchange.
• If deposit interest rate rises to 7%, net interest income
  will fall to 0, but the exchange will pay the bank the
  net value of taking a deposit at 3% = (.07-.03) * ¼ *
  $1M = $1000
• In general, regardless of what the cash rate is on 3-31,
  the sum of the banks net interest income + payment
  from the exchange = $1000. Interest rate risk of the
  loan is eliminated.
                    Example 2
• Selling a future to the exchange is equivalent (in terms
  of income) to contracting a deposit at a guaranteed
  interest rate, the interest rate implied by the current
  price.
• Lets say that a bank would like to make a loan for 2
  years but they must finance this with 3 month time
  deposits.
• To eliminate the interest rate risk, the bank could sell a
  strip of interest rate futures to the exchange with
  settlement dates of 3-31-07, 6-30-07, 9-30-07, 12-31-
  07, ….through the final 3 months that the bank gets
  income eliminating interest rate risk.
                    Basis
• For any interest rate future, there is a
  possibility that the current interest rate
  future will be different from today’s spot
  rate.
• Difference between the cash/spot market
  price and the and the spot price of a future
  is known as the basis.
    Efficient Market Hypothesis &
      Forecasting Interest Rates
• Consider if sellers of an interest rate future believe
  that the cash interest rate will be x% in the future.
  They will be unwilling to pay a higher interest rate
  than x%.
• Consider if buyers believe that the cash interest
  rate will be y% in the future they will be unwilling
  to accept a lower interest rate.
• Purchase price of interest rate futures will be the
  market’s forecast of future spot/cash rate.
• Predicting Future monetary policy Fed Funds
  Futures
  Managing Interest Rate Risk with
       Interest Rate Futures
• When spot interest rate rises, the value of a
  future purchased will fall but the value of a
  future sold will rise.
• Banks net worth will usually decline as
  interest rates rise due to the negative gap.
• If banks sell interest rate futures contracts,
  they can make gains to offset from losses to
  their net worth.
                   Swaps
• Basic (plain vanilla) interest rate swap is
  agreement by two parties to exchange
  interest rate payments on a notional
  principal.
• One party pays a fixed interest rate for a
  pre-determined period of time. Another
  party pays a floating rate equivalent to some
  benchmark interest rate (LIBOR, etc.)
            Schedule of Dealer Quotes
Interest Rate Swap Dealer Quotes for Basic Swaps: Fixed Rate vs. 3 Month LIBOR
March 10. 2005                                        Swap Rates (Fixed Payer Pays)
Term                 US Treasuries                    Bid                   Asked
2 years                    3.83                             4.04                 4.05
3 years                    3.72                             4.18                 4.19
4 years                    3.81                              4.3                 4.33
5 years                       4                             4.52                 4.55
7 years                    4.18                             4.71                 4.74
10 years                    4.3                             4.87                 4.91
20 years                   4.51                             5.13                 5.17
30 years                   4.58                              5.2                 5.28

        Source: Koch and Macdonald, Management of Banking
The dealer will pay LIBOR for the next 2 years to the
customer if the customer will pay a fixed interest rate of
4.05%. The dealer will pay a fixed rate of 4.04% if the
customer will pay LIBOR.
          Swaps and Hedging
• If a bank has long-term fixed rate assets and
  short-term liabilities, they face interest rate
  risk. Solution: Swap income from fixed rate
  assets for floating rate from dealer.
• A pension fund with long-term obligations
  may like to lock in fixed income at a higher
  rate than LT treasuries. They may also swap
  income from floating rate assets for fixed
  income from a dealer.
                       Interest Rate Swaps are Quickly
                            Growing in Importance
                                Interest rate swaps: Notional Principal

                       250000


                       200000
        Billions US$




                       150000


                       100000


                       50000


                           0
                         Ju 9 8



                         Ju 9 9



                         Ju 0 0



                         Ju 0 1



                         Ju 0 2



                         Ju 0 3



                         Ju 0 4



                         Ju 0 5
                         De 998



                         De 999



                         De 000



                         De 001



                         De 002



                         De 003



                         De 004



                         De 005



                                 06
                              20
                              19



                              19



                              20



                              20



                              20



                              20



                              20



                              20
                              1



                              1



                              2



                              2



                              2



                              2



                              2



                              2
                           n.



                           n.



                           n.



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                           n.



                           n.
                           c.



                           c.



                           c.



                           c.



                           c.



                           c.



                           c.



                           c.
                         Ju




Source: BIS International Financial Statistics http://www.bis.org/statistics/derstats.htm
Advantages of Swaps vs. Futures
• Swap terms can be tailored to individual
  needs whereas futures are standarized.
  OTOH, futures markets usually more liquid
  than swap.
• Swaps typically available for longer-terms
  while Futures are short-term.
• Exchange guarantees futures while
                  Options
• An asset that entitles the holder to buy (in
  the case of a call option) or sell (in the case
  of a put option) another asset at a fixed
  price (called the strike price)
• Options last for a limited period of time.
  American options can be exercised any time
  before expiry. European style options are
  only exercised on final date.
                Intrinsic Value
• An option which allows you to buy (sell) at a
  price less (greater) than spot price has value
  since it can automatically be converted into
  cash.
• Intrinsic value is the difference between the
  spot price and the strike price.
• Option with positive Intrinsic Value is “In the
  Money” and negative is out of the money.
                 Put              Call


Intrinsic        Strike Price –   Spot Price –
Value            Spot Price       Strike Price

Strike Price >   In the Money     Out of the Money
Spot Price
Strike Price <   Out of the Money In the Money
Spot Price
              Option Value
• Even if the spot price = strike price, the
  option still has value. The reason: At some
  time in the future, the spot price might
  change putting the option in the money. (If
  the option moves out of the money, owner
  will simply not exercise it).
• Option Price > Intrinsic Value
• Option Price = Intrinsic Value + Option
  Value
                 Option Value
• If the underlying asset price is volatile, there is a
  greater chance that it will move far into the money
  making it more valuable. There will also be a
  greater chance that the option will move far out of
  the money. However, an option that is mildly out
  of the money has an equivalent value to an option
  far out of the money (i.e. zero) since it won’t be
  exercised in either case.
• If the exercise date is far into the future, there will
  also be a greater chance of a movement far into
  the money, increasing option value.
        Measuring Market Risk
• The more risky or volatile a market is, the more
  expensive
• A formula called the Black-Sholes formula is used
  to calculate the value of the option when given the
  expected volatility of an asset.
• Market observers can us the price of options to
  back out the implied expectation of the volatility
  of the market.
                     10.00
                             20.00
                                     30.00
                                             40.00
                                                     50.00
                                                             60.00




              0.00
   12/17/96
   05/19/97
   10/16/97
   03/19/98
   08/18/98
   01/19/99
   06/18/99
 11/16/1999
  4/17/2000
  9/15/2000
 02/15/2001
 07/18/2001
 12/20/2001
 05/23/2002
22-Oct-2002
 03/25/2003
 08/22/2003
 01/23/2004
 06/24/2004
 11/22/2004
  25-Apr-05
                                                                      Implied Volatility Index S&P 100




  9/22/2005
                                                                     Source: Chicago Board of Exchange
    Option Value as Insurance Value
• From the standpoint of a hedger, options can be
  thought of as insurance.
• There may be some change in asset prices that
  might be disastrous for an investor’s portfolio.
  One could buy an option which would be in the
  money if that disastrous price outcome
  occurred, offsetting other losses.
• Like any insurance, the insurer must make an
  upfront payment.
              Interest Rate Caps
• An Interest Rate Cap is conceptually equivalent to
  having the option of accepting a deposit at a pre-
  determined interest rate on the settlement/valuation
  date.
• Net Settlement on Valuation Date: The seller of a Cap
  will pay the difference between the cash rate (i.e.
  LIBOR) and the pre-determined strike rate if the cash
  rate is higher.
• This is equivalent to the upside of buying an interest
  rate future so we think of this as a call option.
             Interest Rate Floor
• An Interest Rate Floor is conceptually equivalent to
  having the option of making a deposit at a pre-
  determined interest rate on the settlement/valuation
  date.
• Net Settlement on Valuation Date: The seller of a
  Floor will pay the difference between the cash rate (i.e.
  LIBOR) and the pre-determined strike rate if the cash
  rate is lower.
• This is equivalent to the upside of selling an interest
  rate future so we think of this as a put option.
 Hedging with Interest Rate Cap
• Assume a bank makes a 1 year loan at a given
  interest rate financed with 3 month time deposits.
• The bank could buy an interest rate cap. If interest
  rates rise in future periods, the bank would receive
  payments which exactly compensate them for
  rising interest costs effectively capping interest
  rates.
• Downside: Must pay premium for this protection.
          Interest Rate Collar
• A bank or firm wishing to restrict the
  interest rate to a certain range will arrange a
  collar
• A collar is the combination of the purchase
  of a cap and the sale of a floor.
  – Zero cost collar is one in which purchase price
    of cap and sale price of floor cancel out.
    Foreign Currency Forwards
• Forward Contracts: Agreements made today
  (t) for an exchange of currency to be made
  at some future date (in T periods).
  – Price, Ft,T determined at time t
  – No money exchanged until time T
• Forward contracts are Over-the-Counter
  (i.e. not traded on an organized exchange)
• Banks are major dealers of FC Forwards.
                Pricing Forward Contracts
• Spot Rate, St = #DCU
  per FCU                   • Two strategies to invest for
• Foreign interest rate for    two periods
  maturity period T, fyt,T    1. Deposit in domestic economy,
                                 return in DCU = (1+yt,T)
• Domestic interest rate      2. Buy foreign currency, deposit
  for maturity period T,         in FC account, sell FC forward
  yt,T                           at rate, Ft,T., return in DCU

                                                                          1
                                                                              (1  fyt ,T )T  Ft ,T
  • Arbitrage implies equal returns for these                             St
  two strategies.

 1                                                      (1  yt ,T )T
     (1  fyt ,T )T  Ft ,T  (1  yt ,T )T  Ft ,T                   St
 St                                                    (1  fyt ,T ) T
                                                 Currency Forwards:
                                                  Mostly short-run
     30000


     25000


     20000                                                                                                                                          Maturity over 5 years

                                                                                                                                                    Maturity over 1 year and up to 5
     15000
                                                                                                                                                    years
                                                                                                                                                    Maturity of one year or less
     10000


      5000


         0
             Jun.98


                               Jun.99


                                                 Jun.00


                                                                   Jun.01


                                                                                     Jun.02


                                                                                                       Jun.03


                                                                                                                         Jun.04


                                                                                                                                           Jun.05
                      Dec.98


                                        Dec.99


                                                          Dec.00


                                                                            Dec.01


                                                                                              Dec.02


                                                                                                                Dec.03


                                                                                                                                  Dec.04




Source: BIS International Financial Statistics http://www.bis.org/statistics/derstats.htm
         Credit Derivatives
• Credit Swaps – Find another bank and swap
  interest & principal payments on two
  different loans.
• Credit Options – Bank’s pay for insurance
  for negative credit events.
                          Credit Swap

     Bank A

                     Loan and Principal



Loan and Principal                             Loan and Principal
                            Intermediary



                          Loan and Principal

                                                    Bank B
                         Credit Option

Bank A
                            Fee Payment




   Payment if negative
   credit event


                                          Bank B
                                Credit Derivatives
                                        Global Credit Derivatives


               14000


               12000


               10000
US$ Trillion




               8000


               6000


               4000


               2000


                  0
                       1H01   2H01   1H02    2H02       1H03        2H03   1H04   2H04   1H05

                  Source: www.credit–deriv.com
              Final Exam
• When: 14/12/06 (THU)
• What time? 08:30-11:30 (am)
• Where? LTC
• What to Bring? Writing Instruments,
  Calculator, Student ID
• What Covered? All Lectures in the course,
  cumulative, 2/3 after the midterm, 1/3
  before.

				
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