Option Pricing Based On CEV Model With Importance Sampling

Constant Elasticity of Variance process (CEV model) is the promotion of the ge-ometric Brownian motion and can describe the behavior of asset prices better. This article examines the pricing of European options and the arithmetic Asian options when the underlying asset follows CEV process by using Monte Carlo simulation pricing method. First, we discrete CEV stock price model and seek a random path for Monte Carlo simulation. And then combined with the Risk Neutral Pricing Theory, we com-plete the pricing process of the call option of the two options without dividend. But Monte Carlo simulation pricing method has the drawback that simulation results are not accurate and have great volatility. So we attempt to adopt the importance sampling, one of the variance reduction techniques, to improve simulation effect. In detail, we ob-tain the optimal parameters of European options and the arithmetic Asian options when the underlying asset follows CEV process by the iterative algorithm. Then the impor-tance sampling function determined by the parameter is applied to the option pricing process. At the end of this article we perform numerical experiments to test the effect of importance sampling. The numerical results show that the calculation method used in this article is feasible and effective.