Option Pricing Under Stochastic Volatility Model

In recent years, the pricing of option in stochastic volatility models has become a research hotspot in this field.The difficulty of the problem and the solving of the complexity compared before have improved a lot level When volatility by constan-t into random. In this way, The theory of option pricing research in stochastic volatility model has the very profound significance.In this paper.we study the problem of the European option pricing and dual currency options pricing under the stochastic volatility models. The main results were as follows:(1)When stochastic volatility satisfy the linear function, we can use traditional Δ hedge technology setting up partial differential equation to satisfy the European option pricing equation. And we can using the martingale method to calculate the solution of series form, if the two random source correlation coefficient in the market satisfying p= 0.(2)when the stochastic volatility satisfy geometric Brown motion process,we can found a new type of equivalent martingale measure Q compared with the mar-tingale measure P in the market. And under this measure, we can calculate the pricing formula of the dual currency options.According to Feynman-Kac formula, could calculate the dual currency options satisfying the model of partial differential equation.