Option Pricing Under Exponential Ornstein-Uhlenbeck Model

Option pricing theory is an important part of modern finance. Scientists have done a lot of researches on traditional Black-Scholes model and obtained significant results which instruct financial practice effectively. Empirical studies show that the expectant are always fluctuant, it is not constant as assumption in Black-Scholes model. Therefore scientists broaden some assumptions of the Black-Scholes model, make various optional model.In order to reflect the movement of stock price better, we consider it obey exponential Ornstein-Uhlenbeck model. In this paper, by means of mathematical tools such as Martingale, stochastic analysis study the exponential Ornstein-Uhlenbeck model, deduce option pricing equations and the corresponding pricing formulas, including stock option pricing, random interest option pricing and lookback option pricing under Ornstein-Uhlenbeck model.The exponential Ornstein-Uhlenbeck model is based on Black-Scholes model, and the option pricing formulas have similar form with Black-Scholes formula. This model reflects the real investment environment better. It is significant work in option pricing research.