Monte Carlo Simulation Methods For Pricing The Asian Options In The CIR Stochastic Volatility Model

In1973, the Fisher Black and Myron Scholes creatively established the first complete option pricing formula. And options market happened historic changes. Later, financial markets are made up of many Different types of financial derivatives. All kinds of new type of options appear constantly, such as Asian options, chooser options, Bermuda options, Barrier options and Reset options,etc. Their prices are more flexible transactions and convenient in marks, more in line with the mark and investors demand. And many financial institutions are continuing to introduce new financial derivatives. How to value these options has become a key topic in modern financial theoretical research and practical application. In the classic Black-Scholes (BS)model,their harsh, idealized hypothesis is that the risk-free rate r and the stock dividend q volatility σ are constant. While in real financial markets, volatility is not constant, and is a stochastic variable that in the market can not directly be observed. Therefore, in order to solve this problem, people treat the volatility as a random pro-cess variables, established stochastic model. This stochastic volatility process relate to the stock price. Stochastic volatility model can deduce un-completely market, avoid the " smile" phenomenon of the volatility, and be better to describe wave clustering features.Asian Option is one of the most common new several options. And is a typical representative in options with strong path dependence, also is one of new options whose is most actively traded in the financial derivatives market at present. Asian options are widely used in International trade of the oil and bond trade, and people get more and more attention in it. This article considers Europe and American Asian options pricing in the CIR stochastic volatility model. Our main contributions are as follows:Chapter1first provides an introduction to the significance and necessity of the pricing option. Second, we introduce the status of the European and American Asian options pricing research at home and abroad, topics basis and so on.In Chapter2, European Asian options pricing in the CIR Stochastic Volatility Models are considered. Underlying stock Price processes meet the geometric Brow-nian motion, the instantaneous volatility processes obey the CIR model, we apply some methods,such as Fourier transform, P.D.E and Feynman-kac formula to obtain the solution of the option price, and we use the Control variable technique Monte Carlo simulation method to calculate the numerical solution of option prices, and had compared the numerical results and analyzed risk characteristics.In Chapter3, In the basis of chapter2, we discuss American Asian options pric-ing in the CIR Stochastic Volatility Models. Through the analysis of pricing Amer-ican options function characteristics, we use the Monte Carlo simulation method to calculate the numerical solution of option prices, and had compared the numerical results.Our main conclusions and the further research works are summarized in Chapter4.