Empirical Applications Of SV Model Based On MCMC Bayesian Method

The B-S pricing formula is the most famous option pricing model all over theworld. It established the foundation of modern option pricing theory. The mostimportant prerequisite is that the volatility of the option price is fixed with strikeprice and term. However, that is not at all the case, especially for the option inand out of the money, the volatility is changing according to strike price andmaturity term, and that is volatility smile and maturity structure which scholarsusually noticed. Thus, it is necessary to have deep research in volatility ifeld andmake adjustment in time.Stochastic Volatility model (SV model) and GARCH model referred in this paperare two of famous model aiming at volatility modeling in the world. Comparedwith GARCH model, SV model has superiorities in many aspects, especially indepicting financial volatility. However, the difficulty of parameter estimation dueto the lack of accurate likelihood function has hindered wide use of SV model.Thanks to the development of simulation technology in recent decades, quantitiesof methods have been raised in dealing with the problems of parameter estimation,and MCMC method based on Bayesian statistics is one of the most popular issues.In comparison with others，the results of MCMC method are more reliable andaccurate. This paper makes research of S&P500index volatility and constructs standardSV model and heavy-tail SV model separately according to Gibbs sampling. Withadvanced prior distribution abroad, this paper gets the estimation of parametersthrough BUGS software and the pass the convergence test. DIC criterion is usedin model comparison and selection process, and heavy tail SV model seems to bemore proper in fitting S&P500volatility. Finally, this paper evaluates forecastingabilities of the above two SV models on basis of RMSE, MAE and LL criterion,taking all the results into account, heavy-tail SV model performs better in fittingS&P volatility.