Pricing American Call Options Under the Assumption of Stochastic Dividends - An Application of the Korn-Rogers-Model

In financial mathematics stock prices are usually modeled directly as a result of supply and demand and under the assumption that dividends are paid continuously. In contrast economic theory gives us the dividend discount model assuming that the stock price equals the present value of its future dividends. These two models need not to contradict each other - in their paper Korn and Rogers (2005) introduce a general dividend model preserving the stock price to follow a stochastic process and to be equal to the sum of all its discounted dividends. In this paper we specify the model of Korn and Rogers in a Black-Scholes framework in order to derive a closed-form solution for the pricing of American call options under the assumption of a known next dividend followed by several stochastic dividend payments during the option's time to maturity.