Pricing Asian Options With Emphasis On Control Variate Monte Carlo Methods

In the theory of options pricing, many important options have not any analytic pricing formulas .It's useful to price them using Monte Carlo simulation methods. But there is big variance,and it's very important that we use Monte Carlo simulation to pricing options. In order to reduce variance, researchers give out many useful reduce variance techniques, such as antithetic variable technique and control variate technique. We must choice different control variates as to different options, so how to choice the control variate is a interesting problem. In this paper ,we discuss the pricing of Asian options and Asian exotic options - - Asian-lookback options, using control variate Monte Carlo simulation, based on the B-S model. And we compare different control variates to choice the better control variate.In Chapter Iand2,we introduce the pricing model of the standard European options, B-S the formulas that we need, and principles of normal Monte Carlo simulation and control variate Monte Carlo simulation. In Chapter 1 and 2,we get the analytic pricing formula of geometric average Asian options and geometric average Asian-lookback options using martingale . As to the arithmetic average Asian options, because of the absence of analytic pricing formula ,here we try to use Monte Carlo method to price it, and use control variate technique . Additionally to reduce the variance of the simulation. For this porpos, we give several control variates firstly, furthermore,we make a emphasis on the numerical analyze of the simulation result with different control variates. As a result of the compare,we choice the geometric average Asian-lookback options and lookback options as the control variate, and make Monte Carlo simulation to price the arithmetic average Asian-lookback options.The research and analysis here have a financial significance. The Asian options and the exotic options are widely used in the different fields of international trade such as petroleum ,traded as afinance tool for risk avoidance and finance management. And Monte Carlo method and the reduce variance technique is a important tool in the options pricing theory.Under the neutral risk, the Asian call options with fixed strike price:C = e-rTE(S - K)+and the put options:P = e-'rTE(K - S)+Sis the average price of the underlying assets during a period (0,T). The Asian-lookback call options with fixed strike price:C — ￡r E(maxQ