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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. n. n. n. n. 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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