Chapter 13 Financial Derivatives © 2005 Pearson Education Canada Inc Hedging Hedge: engage in a financial transaction that reduces or eliminates risk Basic hedging principle: Hedging risk involves engaging in a financial transaction that offsets a long position by taking a short position, or offsets a short position by taking a additional long position © 2005 Pearson Education 13-2 Buying and Writing Calls • A call option is an option that gives the owner the right (but not the obligation) to buy an asset at a pre specified exercise (or striking) price within a specified period of time • Since a call represents an option to buy, the purchase of a call is undertaken if the price of the underlying asset is expected to go up • The buyer of a call is said to be long in a call and the writer is said to be short in a call • The buyer of a call will have to pay a premium (called call premium) in order to get the writer to sign the contract and assume the risk © 2005 Pearson Education 13-3 The Payoff from Buying a Call To understand calls, let's assume that you hold a European call on an asset with an exercise price of X and a call premium of α • If at the expiration date, the price of the underlying asset, S, is less than X, the call will not be exercised, resulting in a loss of the premium • At a price above X, the call will be exercised In particular, at a price between X and X + α, the gain would be insufficient to cover the cost of the premium, while at a price above X + α the call will yield a net profit • In fact, at a price above X + α, each $1 rise in the price of the asset will cause the profit of the call option to increase by $1 © 2005 Pearson Education 13-4 The Payoff from Writing a Call The payoff function from writing the call option is the mirror image of the payoff function from buying the call Note that the writer of the call receives the call premium, α, up front and must stand ready to sell the underlying asset to the buyer of the call at the exercise price, X, if the buyer exercises the option to buy © 2005 Pearson Education 13-5 Summary and Generalization In general, the value of a call option, C, at expiration with asset price S (at that time) and exercise price X is C = max (0, S - X) In other words, the value of a call option at maturity is S - X, or zero, whichever is greater • If S > X, the call is said to be in the money, and the owner will exercise it for a net profit of C - α • If S < X, the call is said to be out of the money and will expire worthless • A call with S = X is said to be at the money (or trading at par) © 2005 Pearson Education 13-6 Buying and Writing Puts A second type of option contract is the put option It gives the owner the right (but not the obligation) to sell an asset to the option writer at a pre specified exercise price • As a put represents an option to sell rather than buy, it is worth buying a put when the price of the underlying asset is expected to fall • As with calls, the owner of a put is said to be long in a put and the writer of a put is said to be short in a put • Also, as with calls, the buyer of a put option will have to pay a premium (called the put premium) in order to get the writer to sign the contract and assume the risk © 2005 Pearson Education 13-7 The Payoff from Buying a Put Consider a put with an exercise price of X and a premium of β • At a price of X or higher, the put will not be exercised, resulting in a loss of the premium • At a price below X - β, the put will yield a net profit • In fact, between X - β and X, the put will be exercised, but the gain is insufficient to cover the cost of the premium © 2005 Pearson Education 13-8 The Payoff from Writing a Put The payoff function from writing a put is the mirror image of that from buying a put As with writing a call, the writer of a put receives the put premium, β, up front and must sell the asset underlying the option if the buyer of the put exercises the option to sell © 2005 Pearson Education 13-9 Summary and Generalization In general, the value of a put option, P, at the expiration date with exercise price X and asset price S (at that time) is P = max (X - S, 0) That is, the value of a put at maturity is the difference between the exercise price of the option and the price of the asset underlying the option, X - S, or zero, whichever is greater • If S > X, the put is said to be out of the money and will expire worthless • If S < X, the put is said to be in the money and the owner will exercise it for a net profit of P - β • If S = X, the put is said to be at the money © 2005 Pearson Education 13-10 How Interest Rate Futures Options Work (see Fig 13-1) Suppose that today you buy, for a $2,000 premium, a European call on the $100,000 June Canada bond futures contract with a strike price of 115 If at the expiration date the underlying Canada bond for the futures contract has a price of • 110, the futures call will be out of the money, since S X, the