European Option Pricing Based on Ornstein-Uhlenback Process under Stochastic Interest Rate

In order to make the stock model and interest rate model closely reflect to the real situation of the financial market,the paper constructed the stochastic differential equation of the stock price whose process was driven by the exponential O-U process.Because it is irrational if interest rate is constant,the interest rate is not risky any more,it always appears to be stochastic changes.In some case that the stochastic interest rate is obeyed the Vasicek interest rate model and under the hypothetical premise of risk-neutral,the unique equivalent martingale measure of O-U process model is found by means of Girsanov theorem from stochastic calculus and by way of the martingale method of pricing options and probability.From the research outcome,the pricing formula of European call option and put option are obtained.The research can imply the certain instruction significance to the market investors.