Option pricing based on a regime switching dividend process

Abstract

This article investigates the European style option valuation under the condition that dividend payments follow a regime switching jump diffusion model while the first l of them have been known. Especially, when l = 0, it follows that all the dividend payments become stochastic. Using the generalized Itô formula, we obtain the explicit solution for dividend payments of the model. From Dividend Discount theory, which implies that the stock price should be equal to the net present value of its all future dividend payments, the stock price process is then deduced. Under the usual pricing framework of derivatives, closed-form solution of European-style option is derived via the characteristic function of the occupation times.