Barrier option pricing for assets with Markov-modulated dividends

Giuseppe Di Graziano, L. C. G. Rogers

Abstract

ABSTRACT

We present a simple methodology to price single and double-barrier options when the dynamics of the underlying stock process follows a geometric Brownian motion with Markov-modulated coefficients and proportional jumps. The non-jumping case follows as a special case. In particular, we show how to derive the Laplace transform (with respect to the time variable) of the barrier price, via solving a system of ordinary differential equations. The method proposed is extremely simple to implement but surprisingly effective. Pricing of doublebarrier options in the classical Black–Scholes framework arises as a special case of the model presented in the paper.