Pricing of general European options on discrete dividend-paying assets with jump-diffusion dynamics

Abstract

• Closed form option prices when underlying asset follows a jump-diffusion process AND pays discrete or continuous dividends. • Distribution of jumps is not specified, so formula includes the cases of lognormal and double exponential distributions. • The pricing formula offers a unified approach to pricing of options in the presence of discrete and continuous dividends. • The formula is written in terms of the Black–Scholes formula, so that the role of the parameters can be inferred. Stocks regularly pay dividends at discrete intervals of time while statistical evidence indicates the existence of small “jumps” in the stock price dynamics. In this paper, we find closed-form solutions for the valuation of European options when the underlying asset is modeled by a jump-diffusion process and pays discrete or continuous dividends. The formula is very general and can be used with any specification on the distribution of the jump. Moreover, the formula is written in terms of the Black–Scholes formula with no jumps or dividends and thus indicates the effect of the jumps and the effect of the inclusion of discrete (or continuous) dividends on the price of the option.