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Unformatted text preview: Chapter 2 An Introduction to Forwards and Options Question 2.1. The payoff diagram of the stock is just a graph of the stock price as a function of the stock price: In order to obtain the profit diagram at expiration, we have to finance the initial investment. We do so by selling a bond for $50. After one year we have to pay back: $50 × ( 1 + . 1 ) = $55. The second figure shows the graph of the stock, of the bond to be repaid, and of the sum of the two positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at expiration is indeed zero. 7 Part 1 Insurance, Hedging, and Simple Strategies Question 2.2. Since we sold the stock initially, our payoff at expiration from being short the stock is negative. 8 Chapter 2 An Introduction to Forwards and Options In order to obtain the profit diagram at expiration, we have to lend out the money we received from the short sale of the stock. We do so by buying a bond for $50. After one year we receive from the investment in the bond: $50 × ( 1 + . 1 ) = $55. The second figure shows the graph of the sold stock, of the money we receive from the investment in the bond, and of the sum of the two positions, which is the profit graph. The arrows show that at a stock price of $55, the profit at expiration is indeed zero. Question 2.3. The position that is the opposite of a purchased call is a written call. A seller of a call option is said to be the option writer, or to have a short position. The call option writer is the counterparty to the option buyer, and his payoffs and profits are just the opposite of those of the call option buyer. Similarly, the position that is the opposite of a purchased put option is a written put option. Again, the payoff and profit for a written put are just the opposite of those of the purchased put. It is important to note that the opposite of a purchased call is NOT the purchased put. If you do not see why, please draw a payoff diagram with a purchased call and a purchased put. 9 Part 1 Insurance, Hedging, and Simple Strategies Question 2.4. a) The payoff to a long forward at expiration is equal to: Payoff to long forward = Spot price at expiration – forward price Therefore, we can construct the following table: Price of asset in 6 months Agreed forward price Payoff to the long forward 40 50 − 10 45 50 − 5 50 50 55 50 5 60 50 10 b) The payoff to a purchased call option at expiration is: Payoff to call option = max [ , spot price at expiration – strike price ] The strike is given: It is $50. Therefore, we can construct the following table: Price of asset in 6 months Strike price Payoff to the call option 40 50 45 50 50 50 55 50 5 60 50 10 c) If we compare the two contracts, we immediately see that the call option has a protection for adverse movements in the price of the asset: If the spot price is below $50, the buyer of the call option can walk away, and need not incur a loss. The buyer of the long forward incurs a loss, while he has the same payoff as the buyer of the call option if the spot price is above $50. Therefore, thehe has the same payoff as the buyer of the call option if the spot price is above $50....
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This document was uploaded on 03/28/2011.
 Spring '11

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