© K.Cuthbertson, D. Nitzsche1 Version 1/9/2001 FINANCIAL ENGINEERING: DERIVATIVES AND RISK MANAGEMENT (J. Wiley, 2001) K. Cuthbertson and D. Nitzsche LECTURE Derivatives: An Overview

© K.Cuthbertson, D. Nitzsche2 Forwards and Futures Contracts Options Contracts Swaps Topics

© K.Cuthbertson, D. Nitzsche3 Forwards and Futures

© K.Cuthbertson, D. Nitzsche4 The buyer(long) in a forward/futures contract: u acquires a legal obligation to buy an asset (the underlying)  at some specific future date (maturity/expiry date)  in an amount (contract size).  and at a price (the forward/futures price) which is fixed today. Forward/Futures Contract

© K.Cuthbertson, D. Nitzsche5 Hedging (removing risk) In Jan. MacDonalds purchases a forward contract for delivery of live cattle in December at price fixed today ~ holds to maturity Speculation Buy a 3m futures contract today at F 0 =$100 and sell after 1m at F=$110 ~ close out contract (no delivery) and profit of $10. Arbitrage Keeps movement of F in line with S (underlying) Uses of Forward/Futures Contract

© K.Cuthbertson, D. Nitzsche6 ContractExchangeContract Size 1.Grains and Oilseed CornCBOT5,000 bu WheatMCE1,000 bu 2.Food CocoaCSCE10 metric tons Orange NYCTN15,000 lbs 3.Metals and Petroleum GoldMCE33.2 troy oz SilverCBOT5,000 troy oz 4.Livestock and Meat HogsCME50,000 lbs Pork Bellies CME40,000 lbs Futures Contracts

© K.Cuthbertson, D. Nitzsche7 ContractExchangeContract Size 5.Foreign Currency British PoundIMM£ 62,500 Swiss FrancCMESFr125,000 EuroCMEEuro 125,000 Japanese YenCME Yen12.5m 6.Stock Indices S&P500IOM$500 x Index Value LineKCBT$500 x Index FTSE100LIFFE£10 x index Eurotop100LIFFEEuro 20 x index Nikkei 225IOM$5 x Index Futures Contracts

© K.Cuthbertson, D. Nitzsche8 ContractExchangeContract Size 7.Interest Rates Eurodollar - 90 dayIMM$ 1,000,000 Euromark IMMDM 1,000,000 US T-Bills IMM$ 1,000,000 US T-Bonds CBOT$ 100,000 UK 3m-Sterling Int rateLIFFE£500,000 UK 3m EuroLIBOR LIFFEEuro 1m UK Long Gilt FutureLIFFE£100,000 CBOT = Chicago Board of Trade CME = Chicago Mercantile Exchange NYCE= New York Cotton Exchange IMM= International Money Market (Chicago) LIFFE=LondonInternational Financial Futures Exchange Futures Contracts

© K.Cuthbertson, D. Nitzsche9 FORWARDSFUTURES Private contractTraded on an exchange Delivery at expiry Usually closed out before maturity Usually one delivery dateRange of delivery dates No cash paid until expiryCash payments Daily( margin) Negotiable choice of delivery dates, size of contract Standardised Contract Comparison of Forwards and Futures

© K.Cuthbertson, D. Nitzsche10 Options Contracts

© K.Cuthbertson, D. Nitzsche11 Holder has the right to buy or sell an ‘asset’ (underlying) at some time in the future at a fixed price but she does not have to exercise this right can ‘walk away’ from the contract if holder wishes ~ latter is key distinction between options and futures/futures contracts. E.g. In Jan, purchase an option to buy 100 Microsoft shares in September, at a fixed price of $102 What happens in Sept if actual stock price is $90 or $110? Options

© K.Cuthbertson, D. Nitzsche12 Insurance (form of hedging) e.g. can insure a minimum selling price for a stock, at maturity of the option contract (e.g. in 6m time), but can also benefit from higher prices should these occur Speculation Can buy an option at a ‘low’ price and may be able to sell it (before maturity) at a ‘high’ price ~ close out the position (hence no delivery at maturity) Arbitrage Keeps option price and price of underlying (e.g. stock) moving (broadly) together (but not ‘one-for-one) Uses of Options

© K.Cuthbertson, D. Nitzsche13 ContractExchange Contract Size 1.Individual Stocks BOE, NYSE, AMEX, PHSE, LIFFE, SIMEXUsually 100 stocks 2. Index Options S&P500 Index CBOE $500 x index FTSE100 Index LIFFE £10 per index point NYSE Index NYSE $500 x index Foreign Currency Options Sterling PHSE GBP 31,250 Deutsche Mark PHSE DEM62,500 Japanese Yen PHSE JPY6.25m Canadian Dollar PHSECND50,000 Swiss Franc PHSECHF62,500 Options

© K.Cuthbertson, D. Nitzsche14 ContractExchangeContract Size 3.Options on Futures Contracts Options on interest rate futures: Eurodollars IMM $1m US T-Bills IMM $1m US T-Bond CBOT $100,000 3-month EuroLIBOR LIFFE as for futures UK Long Gilt LIFFE as for futures Options on index futures: S&P500 IndexIOM$500 x premium Nikkei 225IOM$5 x premium Most commodities (agriculture and metals) on which there are futures contracts (see above).CBOT,CME,KCBT, COMEX,CTNThe same as in the futures contract Options

© K.Cuthbertson, D. Nitzsche15 A European call option gives the holder (the long) the right (but not an obligation)  to purchase the underlying asset at a  specified future date (known as the expiration, expiry or maturity date)  for a certain price (the exercise or strike price)  and in an amount (contract size) which is fixed in advance.  For this privilege you pay today, the call premium/price. Call Option

© K.Cuthbertson, D. Nitzsche Figure 1.1 : Buy one European Call Option STST Profit Strike price K = $80 $5 -$3 Call premium $88$83 K = $80 0

© K.Cuthbertson, D. Nitzsche Figure 1.8 : Leverage from option (on 100 shares) OPTIONS MARKET (JULY) Call premium, C = $3 Premium paid = $300 Strike price, K = $80 CASH MARKET (JULY) Spot price, S = $78 Cash paid = $7800 OPTIONS MARKET (OCT.) Profit = $8 = ($88 - $80) Net profit = $800 - $300 Return = $500/$300 = 167% CASH MARKET (OCT.) Profit = $10 = ($88 - $78) Total profit = $1000 Return = $1000/$7800 = 12.8%

© K.Cuthbertson, D. Nitzsche Figure 1.2 : Sell (write) a European Call Option STST Profit Strike price K = $80 -$5 $3 Call premium $88 $83 K = $80 0

© K.Cuthbertson, D. Nitzsche19 A European put option gives the holder (the long) the right (but not an obligation)  to sell the underlying asset at a  specified future date (known as the expiration, expiry or maturity date)  for a certain price (the exercise or strike price)  and in an amount (contract size) which is fixed in advance.  For this privilege you pay today, the call premium/price. Put Option

© K.Cuthbertson, D. Nitzsche Figure 1.3 : Buy (long) a European Put Option Strike price K = $70 STST Profit $3 -$2 Put premium $68 $65K = $70 0

© K.Cuthbertson, D. Nitzsche Figure 1.4 : Sell (write) a European Put Option Strike price K = $70 STST Profit $2 -$3 Put premium $68 $65 K = $70 0

© K.Cuthbertson, D. Nitzsche Swaps

© K.Cuthbertson, D. Nitzsche Figure 1.5 : Liabilities : Using Swaps Swap A negotiated (OTC) agreement between two parties to exchange cash flows at a set of pre-specified future dates Plain Vanilla Interest Rate Swap M/s A. agrees to pay interest at a floating rate and receive fixed rate payments from the “other side” of the swap transaction (eg. M/s B) e.g. 5 year swap, with floating rate at 6m LIBOR, with resets every 6 months. Fixed rate is say 5% p.a. Usually the interest payments are in the same currency

© K.Cuthbertson, D. Nitzsche Figure 1.5 : Liabilities : Using Swaps Floating to Fixed: Liability Fixed to Floating :Liability Issue Floating Rate Bond Firm’s Swap LIBOR LIBOR + 0.5% 6% fixed Net Payment = 0.5% + 6% = 6.5% (fixed) Issue Fixed Rate Bond Firm’s Swap 6% fixed 6.2% fixed LIBOR Net Payment = 0.2% + LIBOR (floating)

© K.Cuthbertson, D. Nitzsche Figure 1.6 : Assets : Using Swaps Floating to Fixed: Asset Fixed to Floating: Asset Hold Floating Rate Bond Firm’s Swap LIBOR LIBOR - 0.5% 6% fixed Net Receipts = 6% - 0.5% = 5.5% (fixed) Hold Fixed Rate Bond Firm’s Swap 6% fixed 5.7% fixed LIBOR Net Receipts = LIBOR - 0.3% (floating)

© K.Cuthbertson, D. Nitzsche Figure 1.7 : Swap : financial intermediary Hold Floating Rate Bond Firm’s Swap 11% fixed 12% fixed LIBOR After swap : Net Receipts = (12% - 11%) + LIBOR - (LIBOR - 1%) = 2% (fixed) LIBOR - 1% Without swap if LIBOR > 13% firm’s swap makes a loss.

© K.Cuthbertson, D. Nitzsche End of Slides