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Quantitative Finance by Matt Davison

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Chapter 27

Black Scholes with Dividends

27.1 CHAPTER SUMMARY

Section 27.2 explains modeling the impact of dividends on stock prices. Both discretely paid dividends (the realistic case) and continuously paid dividends (the mathematically tractable case) are considered. Then, in Section 27.3, a Black Scholes-like PDE for the value of a European derivative written on a dividend paying stock is derived for the continuous dividend payment. Section 27.4 solves the so-called “linear” derivative of a prepaid forward on the stock. Section 27.5 concludes with a trick which allows the solution of the no dividend option to be transformed to obtain the solution of the dividend paying option.

27.2 Modeling Dividends

What are dividends and why are they paid? ...

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