Option Pricing Under The Volatility Based On Bayesian Methods

For the hypothesis about the volatility is constant in the classic Black-Scholes option pricing model which inconsistent with reality,and GARCH models can describe the time-varying of volatility very well,so there are many scholars consider about GARCH models.The biggest difference between Bayesian method and the traditional statistical methods is the former assumes that the all parameters are random variables rather than fixed values.Moreover,Bayesian method combines prior informations and sample information is more reasonable than the traditional statistical methods,so we conduct the statistical inference of models' by Bayesian method in this article.Domestic researches on GARCH models are mainly applied in financial assets' yield,and hardly combine with Bayesian mothod and application of Option Pricing.We mainly study about GARCH and asymmetric GARCH models with Student errors,and their applications in the option pricing.this article's work are following:1.On the basis of the GARCH option pricing model,we use GARCH and asymmetric GARCH models with Student errors to studyoption pricing,and we give the Bayesian computing methods to calculate the price of option.2.This article also get the theoretical Bayesian inference of GARCH and asymmetric GARCH models with Student errors.With the rational prior information,we obtain all parameters' conditions posterior distribution in both models.We also give the algorithms to sampling from the conditions posterior distribution.In this article,we consider the problem of the uncertainty of model,and conduct the statistical inference on option's price by using Bayesian model averaging.This can avoid the problem of model's bias caused by the uncertainty of model,so that we can offer a more comprehensive view to analyze the problem.This article's work get the theoretical preparation for the empirical study in future,and give the specific numerical methods.