Option Pricing Under Exponential Ornstein-Uhlenbeck Model

Option pricing theory is an important part of modern finance.Together with the portfolio selection theory,the capital asset pricing theory,the effectiveness theory of market and acting issue,it is regarded as one of the five theory modules in modern finance.Many scholars have done a great deal of researches on Black-Scholes model and obtained a lot of results which is instructive to financial practice.However,supposing that the process of stock price is of lognormal distribution,invariable expectant yields means movement of stock price towards just one direction along with the change of time.Demonstration studies have indicated that the expectant yields of stock prices arc always fluctuant,and may be functions depending on time and stock prices.Therefore,many scholars put forward all kinds of option pricing models by relaxing some assuming conditions of Black-Scholes model.In this dissertation,We consider exponential Ornstein-Uhlenbeck model,which correspond to the actual characteristics of stock price movement better.That is,parameter α cause downtrend of stock price while rising to some degree.This dissertation study option pricing problems under exponential Ornstein-Uhlenbeck model by means of mathematical tools such as martingale theory and stochastic analysis,provide the pricing formula of lookback options,make prices of exponential Ornstein-Uhlenbeck model under the hypothesis of stochastic interest rate,and establish an generalized exponential Ornstein-Uhlenbeck model with "jump" ,to deduce the option value equation and the option pricing formula.In detail we have made main conclusions as follows:(1)Under the hypothesis of exponential O-U model and constant interest rate ,using risk-neutral pricing principle, we obtain the pricing formulas of lookback option in two cases of fixed strike price and floating strike price,and the put-call parity relation is deduced;(2)Under the hypothesis of exponential O-U process model and continuous stochastic interest rate,we obtain the option value equation and the pricing formula of European call option;(3)Under the hypothesis of exponential O-U process model and incontinuous stochastic interest rate,we obtain the option value equation and the pricing formula of European call option;(4)We establish an generalized exponential O-U model with "jump" ,and the option value equation and the pricing formula of European call option are deduced under incontinuous stochastic interest rate model.