Abstract
This paper compares the American option prices with one known dividend under two alternative specifications of the underlying stock price: displaced log normal and log normal processes. Many option pricing models follow the standard assumption of the Black–Scholes model (Journal of Political Economy 81:637–659, 1973) in which the stock price, follows a log normal process. However, in order to reach a closed form solution for the American option price with one known dividend, Roll (Journal of Financial Economics 5:251–258, 1977), Geske (Journal of Financial Economics 7: 63–81, 1979), and Whaley (Journal of Financial Economics 9:207–211, 1981) assume a displaced lognormal process for the cum-dividend stock price which results in a lognormal process for the ex-dividend stock price. We compare the two alternative pricing results in this paper.
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