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The appendix derives the key result: E[max(VK,0)]=E(V)N(d 1 ) KN(d 2 ). Show that E[max(KV,0)]=KN(d 1 )

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The appendix derives the key result: E[max(V−K,0)]=E(V)N(d1) −KN(d2). Show that

E[max(K−V,0)]=KN(­−d1) −E(V)N(−d2)

and use this to derive the Black-Scholes-Merton formula for the price of a European put option on a non-dividend-paying stock

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The easiest way of proving this is to note that max V K 0 max K V 0 VK so that E max K ...View the full answer


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Options Futures and Other Derivatives

Options Futures and Other Derivatives

ISBN: 978-0134472089

10th edition

Authors: John C. Hull

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A put option is a financial contract that gives the owner the right, but not the obligation, to sell an underlying asset, such as a stock or a commodity, at a predetermined price, known as the strike price, on or before a specific date, known as the expiration date. Put options are used by investors as a form of insurance against a decline in the value of the underlying asset. If an investor expects the value of an asset to fall in the future, they can purchase a put option on that asset. If the value of the asset does fall, the put option will increase in value, allowing the investor to sell the asset at the higher strike price. For example, if an investor owns 100 shares of a stock that is currently trading at $50 per share, they may purchase a put option with a strike price of $45 and an expiration date three months in the future. If the stock price falls to $40 before the expiration date, the investor can exercise the put option and sell their shares for $45 each, even though the market price is only $40. This would allow the investor to limit their losses. It\'s important to note that purchasing a put option involves paying a premium to the seller of the option, and the investor can lose the entire premium if the price of the underlying asset does not decline as expected. Put options are just one type of financial derivative and should only be used by experienced investors who understand the risks involved.

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