M02_MCDO8122_01_ISM_C02

M02_MCDO8122_01_ISM_C02 - Chapter 2 An Introduction to...

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Chapter 2 An Introduction to Forwards and Options n 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 incorporate the initial costs of the stock, i.e., how we finance the initial investment. We do this by assuming we borrow $50 at 10% interest. Note that even if we use our own funds to finance the purchase, we want to incorporate the opportunity costs of our investment (i.e., the interest we could have earned). By borrowing $50, after one year we have to pay back: $50 (1 0.1) $55. × + = The second figure shows the graph of the stock, the $55 we have to pay back, 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. When the stock price is $55, our stock is worth exactly what we owe and, hence, we break even.
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10 McDonald • Fundamentals of Derivatives Markets n Question 2.2 Since we shorted the stock initially, our payoff at expiration is negative and equal—the stock price. This is the amount we have to spend in order to replace the share of stock we borrowed.
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Chapter 2 An Introduction to Forwards and Options 11 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 0.1) $55. × + = The second figure shows the graph of the payoff of the shorted stock, the money we receive from the investment in the bond, and 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. At $55, the amount of money we receive from our bond investment is exactly offset by the amount of money we need to buy back the one share of stock we borrowed. n 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 in the call option. 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. n Question 2.4 1. The payoff to a long forward at expiration is equal to: Payoff to long forward Spot price at expiration forward price = -
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12 McDonald • Fundamentals of Derivatives Markets 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 0 55 50 5 60 50 10 2. The payoff to a purchased call option at expiration is: Payoff to call option max[0, spot price at expiration
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