The Pricing And Applications Of Product Option

In recent years,financial derivatives have developed rapidly throughout the world.The option is one of the most popular derivatives.A number of different types of options have attracted more and more traders.And many mathematician and economists pay more attention to price options.In the 1970 s,Black and Scholes first proposed the B-S model.But some of the assumptions do not fully reflect certain phenomena in the real market.Many scholars extended the B-S model,for example,from constant value of dividend rate,drift rate and volatility to definite functions of time ,from continuous asset price process to jump-diffusion process and from constant interest rate to stochastic interest rate.The product option,which is an option written on the product of two underlying assets prices or indices,is widely traded in the market.The foreign domestic option and the company's revenue option are the special product option.In this paper,we study the pricing of product option under extended B-S models.The main content is as follows.First,we suppose that the underlying asset price follows the geometric Brownian motion,the risk-free interest rate r(t),the drift rate ?(t)and the volatility ?(t)of the asset are definite functions of time .By using the property of It(?) integral,we obtain the pricing formula.Then we discuss some applications of product option.Second,we suppose that the underlying asset price follows the Jump-Diffusion process,r(t),?(t)and ?(t)are definite functions of time .By using the property of It(?) integral and Possion process,we obtain the pricing formula of product option.Third,we suppose that the underlying asset price follows the Jump-Diffusion process,and r(t)follows the Vasicek model.By using the method of measure transformation,we obtain the pricing formula of product option.