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Consider the following SDE that governs asset prices in our model: dSt = Stdt + StdWt (24.59)

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Consider the following SDE that governs asset prices in our model:
dSt = μStdt + σStdWt (24.59)
Assume that the risk-free interest rate is 3% and that there are no dividends in the model. Further, assume the current stock price is $70. Write a program that prices a one-year American put option struck at $55 in the above framework. Make sure that the optimal exercise decision is included in the tree.
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The following code can be used to price an American ...View the full answer


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Ali Khawaja
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An Introduction to the Mathematics of Financial Derivatives

An Introduction to the Mathematics of Financial Derivatives

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Authors: Ali Hirsa, Salih N. Neftci

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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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