9. (Dividend-Paying Options) Based on the code in Section 12.4.3 and the BlackScholes formula, compute the following

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9. (Dividend-Paying Options)

Based on the code in Section 12.4.3 and the Black–Scholes formula, compute the following perpetual option values:

 American call and put with and without dividends.

 European call and put with and without dividends.

Optimise the code in Section 12.4.3 to create a single function that computes both call and put American option prices and that returns their values in a tuple.

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