A Research And Analysis On Numeric Methods For Option Pricing Under Levy Process

In option pricing, if the precise analysis formula of pricing derivative is unable to be obtained under many situations, it is useful to get option prices through numerical methods. This article makes research and analysis to numerical methods for option pricing respectively, which mainly include the Binomial Trees, the Trinomial Trees, the finite difference method, the Monte Carlo method as well as the neural network and so on, under the assumption that price vibration of stocks satisfies two different Levy processes, which are Winner process and Jump Diffusion process, by taking MATLAB as a computation tool. When uses each numerical method for pricing options, not only analysis of various method parameters on stock prices, but also consider influence of paramteres impact on method itself, for example: Convergence rate, stability and so on.This article mainly includes 5 parts as follows:In the first part, it introduces topic background, research significance, each kind of option pricing theory, by the scheduled time power fixed price theory and numerical method development course.In the second part, it mainly proposes each value computational method, and carries on the detailed introduction to each value method.The third part mainly uses each kind of value computation separately the method to price the different type of options, when the stock price undulation satisfies Winner process. And we carry on the parameter analysis, the comparison to each numerical method. As well as separately simulation makes the improvement to the Binomial Trees and Monte the Carlo, after the improvement algorithm no matter is the undulation scope or the convergence rate and the precision all has the distinct enhancement.The fourth part mainly introduces the option pricing when the stock price undulation satisfies Jump Diffusion process. Firstly, we introduce the jump Diffusion model theory, in view of extent of jump Y the different distribution which the scope satisfies, considers the binomial distribution, the log-normal model and the double index model separately. And simulates through Monte Carlo carries on the value computation and the analysis, and analyzes each parameter to the time power value influence.The fifth part mainly introduced the BP neural network in the option pricing utilization, accepts in the Winner process, regarding American Put option and Lookback option, after carries on the training to forecast, through the real diagnosis indicated this BP network model has certain reliability; all may use in the time power the fixed price. But in jumps in the diffusion processs, if will take the input parameter λ, then discovered the BP network will not necessarily have reliably, namely will work as when very big, the network will not be able to forecast.Finally, summarizes this article, and proposes new ideas in broadening this study.