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Option Pricing and Estimation of Financial Models with R by Stefano M. Iacus

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Chapter 7

American options

7.1 Finite Difference Methods

American options are similar to European options with the peculiarity that they can be exercised during the whole time interval images/c07_I0071.gif.

Assume that we own an American call contract with a strike price of 40 images/euro.jpg, expiry date one month and the current price of the underlying asset is 50 images/euro.jpg.

If this is the case, it will appear very profitable to exercise the option immediately and gain 10 images/euro.jpg. But, if we also own a portfolio which includes the underlying asset of this option and we want to keep it for at least one month, then exercising now is not the best strategy. So we want to wait a little more.

Another good reason to wait is that there is still some probability (even if very small) that the price of the underlying asset decreases below 40 images/euro.jpg; in such a case the American call option plays the role of a warranty against the decrease in value of the assets in our portfolio.

On the contrary, if we think that the asset in our portfolio is overvalued ...

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