Monte Carlo Method Is Applied Research In The Pricing Of Financial Derivatives

In the current financial markets, the kinds of major financial derivatives such as option have became more and more various, the individuating demands of various customers need more and more financial instruments, impact of financial liberation, financial innovation and global financial integration .With the rapid development of singular and advanced derivative securities, the method of real options based on option pricing theory is being taken more seriously. These trends make the financial markets need a powerful mathematical tool to solve the problem of financial derivatives pricing urgently. The Monte Carlo method has such features, simple program structure, the probability of convergent and Independent of the convergence rate and the problem dimension. It is more and more used in the option pricing because of making up the lack of grid analysis and finite-difference technology in the face of high-dimensional problem. This paper introduces the background knowledge of option pricing, and summarizes the current method of option pricing, and gives the general theory of Monte Carlo, including the generation of random numbers and variance reduction techniques.This article focuses on the variance reduction technique which is the Monte Carlo simulation of a major research direction in the world. Based on their achievements, these technologies will be applied to the simulation of the singular options pricing, and the realization of these algorithms program are given. From the text's calculated example, it seems that these technologies are effective; significantly reduce the variance estimator; enhance the effectiveness of the estimator; improve the efficiency of the simulation.To expand the scope of application of Monte Carlo simulation, the first is the expansion of the type of derivative securities, the simulation method's pricing applications are broaden to American options, Asian options and so on, whose derivatives securities are more complex; the second is extended the simulation to the applications which is based on the assumption of the complex subject of the process assets, such as the classical assumption of Black-Sholes is extended to the complex assumptions of stochastic volatility, random jump-diffusion that belong to derivatives securities pricing.The applications of variance technology mentioned in this article have the mathematics tests on computer, and show their validity.