MH-BSL Method And Its Application In Stochastic Volatility Model

In the financial market,fluctuation refers to the variability of financial assets in a certain period of time.Statistically,it is usually measured by the standard deviation of its price rise and fall within a year.Volatility refers to the degree of price fluctuation of financial assets(including stocks,bonds and interest rates).Volatility is essentially unobservable,that is,we cannot know its fair value.We can only estimate the volatility of assets in a certain historical stage based on the standard deviation of the profits and losses of the underlying assets.Modeling volatility and solving risk management and pricing of derivatives have always been difficult points in the financial market.The price of financial assets is usually modeled by time series.The volatility of time series is mainly analyzed by two types of models: generalized autoregressive conditional heteroscedasticity(GARCH)model and stochastic volatility(SV)model.Compared with GARCH model,SV model has been proved to have some theoretical advantages,such as smaller pricing difference and better fitting effect on ”volatility smile”.However,because the likelihood of SV model is not analytically expressed,the traditional maximum likelihood estimation cannot be used for parameter estimation,and the complexity of Bayesian estimation based on MCMC method hinders its wide use to a certain extent.In this paper,a new estimation method,Bayesian synthetic likelihood method based on MH sampling(MH-BSL),is proposed.MH is an efficient posterior distribution sampling method,and BSL can solve the situation that the likelihood function is complex and difficult to deal with.The combination of the two can effectively solve the estimation problem of stochastic volatility model,making the Bayesian analysis of SV model more rapid and accurate.Two practical examples are given to illustrate the feasibility and effectiveness of MH-BSL algorithm.Compared with the traditional Bayesian synthetic likelihood(BSL)method,MH-BSL algorithm can effectively make up for the shortage of fitting volatility only with BSL method,and can ensure the accuracy and running time of parameter estimation under the new algorithm.Aiming at the characteristic of peak and thick tail in financial market,we also apply MH-BSL algorithm to SV-Stable model to further verify its feasibility and effectiveness.The research of this paper shows that MH-BSL algorithm can realize more effective and faster parameter estimation of SV model,and can be used to solve the related problems of financial asset volatility.