The Research Of Two Asset Options Pricing On Jump-Diffusion Process Model

In modern financial markets, financial derivatives is very popular for its strong functionality of avoiding risk and hedging. Options is an important financial derivatives which is widely used. Therefore the research about options has aroused the concern of the majority of experts and scholars. With the strengthening of standardized construction and the accelerating of internationalization pace in the options market of our country, the importance and urgency of the study about option pricing is increasing and the study has great significance.This paper investigates the pricing of the European option to exchange one asset to another and the two asset European better(worse)-of options. It is on the basis of the jump-diffusion model proposed by Merton which is on the assumption that the stock pricing processes are jump-diffusion processes, and the jump processes are homogenous Poisson process. The differential equations of option value when the stock pricing pocesses has both dividends payment and non-dividends payment is derived with no-arbitrage theory. By using the theory of equivalence martingales measure and the method of numeraire conversion, selecting the appropriate risk-neutral probability measure, the problem of the two-dimensional asset option pricing is transformed into that of a one-dimensional asset option pricing. So we could obtain the exact formula for pricing exchange option by using the original conclusions. Then the formula for pricing two asset better(worse)-of options is obtained with the same method. We choose the jump-diffusion process model rather than the classical Black-Scholes diffusion process model, and compare the conclusion of the two. Facts have proved that the formula of option pricing is easily obtained in the jump-diffusion models with the theory of equivalence martingales measure and the method of numeraire conversion which is also used in the diffusion models.