A summary on pricing American call options under the assumption of a lognormal framework in the Korn-Rogers Model

In accordance with a variety of option pricing models and the economic approach of the dividend discount model, Korn and Rogers [Stocks paying discrete dividends: modelling and option pricing, Journal of Derivatives 13 (2005), 44-49] have introduced a general dividend model preserving the stock price to follow an exponential Lévy process and to be equal to the sum of all its discounted dividends. In this paper we use the model of Korn and Rogers in a Black-Scholes framework to derive a closed-form solution for the pricing of American Call options under the assumption of a possibly known next dividend followed by several stochastic dividend payments during the option's time to maturity.