European Option Pricing with Discrete Stochastic Dividends

The original Black-Scholes model prices options on a non-dividend paying stock, but of course, most actual stocks pay dividends. The two standard ways of adjusting for dividends are either to assume future dividends are known with certainty and subtract their present value from the current stock price, or to assume the dividend is paid continuously as a constant proportion of the stock price (making the dividend amount stochastic). This article shows that even when dividends are discrete and stochastic, the first type of dividend correction can still work. The key is that the current market values of the stochastic future dividends must be subtracted from the initial stock price. Chance, Kumar, and Rich then discuss ways in which the necessary market values might be obtained.