Research Of Monte Carlo Methods In Option Pricing

Financial derivative security has gained worldwide popularity and development in the pasta few years. Fueled by its success, the problem of contingent claims valuation has receivedconsiderable research attention. Option Pricing Theory (OPC) even becomes the third theorythat won the Nobel Prize in Economics after Asset Portfolio Theory (APT) and Capital AssetPricing Model (CAPM). As a basic financial derivative, there are a number of major methods ofvaluation of contingent, such as, Partial differential equations method、Martingale Method andNumerical method；Likewise, There are several different Numerical methods, such as, Binarytree method、Finite difference method and Monte Carlo method used by this paper.In this paper, R language and Monte Carlo method are combined to solve the valuation ofcontingent under different models efficiently. The basic theories of contingent are introducedand the general methods of valuation of contingent as well. The superiority of Monte carlomethod is presented. Moreover, the valuation of contingent under stochastic rates models andstochastic volatilities models are illustrated and compared with that under Partial differentialequations method, and is verified by the experiment results.What’s more, Propose doublestochastic models creatively, and is verified more effective than other models.