Question

Use the result in equation (15.17) to determine the value of a perpetual American put option on a non-dividend-paying stock with strike price $K$ if it is exercised when the stock price equals $H$ where $H<K$. Assume that the current stock price $S$ is greater than $H$. What is the value of $H$ that maximizes the option value? Deduce the value of a perpetual American put with strike price $K$.

   Use the result in equation (15.17) to determine the value of a perpetual American put option on a non-dividend-paying stock with strike price $K$ if it is exercised when the stock price equals $H$ where $H<K$. Assume that the current stock price $S$ is greater than $H$. What is the value of $H$ that maximizes the option value? Deduce the value of a perpetual American put with strike price $K$.

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 15, Problem 23

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Step 1

According to equation (15.17), the value of a perpetual American put option is given by: $V = \frac{K}{r} - \frac{S}{r} + \frac{S}{r} \cdot \frac{1}{1 - \frac{H}{S}}$ Substituting $H$ for $S$ in the equation, we get: $V = \frac{K}{r} - \frac{H}{r} + Show more…

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Use the result in equation (15.17) to determine the value of a perpetual American put option on a non-dividend-paying stock with strike price $K$ if it is exercised when the stock price equals $H$ where $H<K$. Assume that the current stock price $S$ is greater than $H$. What is the value of $H$ that maximizes the option value? Deduce the value of a perpetual American put with strike price $K$.

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