015 - 15 American Option Pricing Answers to Questions and...

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142 Answers to Questions and Problems 1. Explain why American and European calls on a nondividend stock always have the same value. An American option is just like a European option, except the American option carries the right of early exercise. Exercising a call before expiration discards the time value inherent in the option. The only offsetting benefit from early exercise arises from an attempt to capture a dividend. If there is no dividend, there is no incentive to early exercise, so the early exercise feature of an American call on a nondividend stock has no value. 2. Explain why American and European puts on a nondividend stock can have different values. The exercise value of a put is X 2 S . On a European put, this value cannot be captured until the expiration date. Therefore, before expiration, the value of the European put will be a function of the present value of these exercise proceeds: e 2 r ( T 2 t ) ( X 2 S ). The American put gives immediate access at any time to the full proceeds, X 2 S , through exercise. In certain circumstances, notably on puts that are deep-in-the-money with time remaining until expiration, this differential in exercise conditions can give the American put extra value over the corresponding European put, even in the absence of dividends. 3. Explain the circumstances that might make the early exercise of an American put on a nondividend stock desirable. Early exercise of an American put provides the holder with an immediate cash inflow of X – S . These proceeds can earn a return from the date of exercise to the expiration date that is not available on a European put. However, early exercise discards the time value of the put. Therefore, the early exercise decision requires trading off the sacrificed time value against the interest that can be earned by investing the exercise value from the date of exercise to the expiration date of the put. For deep-in-the-money puts with time remaining until expiration, the potential interest gained can exceed the time value of the put that is sacrificed. 4. What factors might make an owner exercise an American call? The key factor is an approaching dividend, and exercise of an American call should occur only at the moment before an ex-dividend date. The dividend must be “large” relative to the share price, and the call will typically also be deep-in-the-money. 15 American Option Pricing
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5. Do dividends on the underlying stock make the early exercise of an American put more or less likely? Explain. Dividends make early exercise of an American put less likely. Dividends decrease the stock price and increase the exercise value of the put. Thus, the holder of the American put has an incentive to delay exercising and wait for the dividend payments. 6. Do dividends on the underlying stock make the early exercise of an American call more or less likely?
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015 - 15 American Option Pricing Answers to Questions and...

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