Analytical Valuation of Asian Options with Continuously Paying Dividends in Jump-Diffusion Models

Abstract

We consider the problem of valuation of certain Asian options in the geometric jump-diffusion models with continuously dividend-paying assets. With the sources of diffusion risks and two primitive tradeable assets, the market in this model is, in general, incomplete, and so, there are more than one equivalent martingale measures and no-arbitrage prices. For this jump-diffusion model, we adopt the minimal martingale measure as the risk-neutral pricing measure for option valuation in a dynamically incomplete market. A partial integro-differential equation satisfied by the no-arbitrage price of an Asian option is obtained by change of numeraire technique under the minimal martingale measure.