Improvement And Application Of MCMC Method For Paramter Estimation Of SV Models

Volatility modeling is a hot issue in the financial market in recent decades.In the volatility model,the stochastic volatility(SV)model has a wide range of applications.The introduction of random variables in the SV model,whether from the predictive ability of long-term volatility,or from the stability of volatility sequences or the application of asset pricing theory,is more advantageous than other volatility models.The SV model contains latent variables,and the likelihood function and unconditional moments involved are calculated by high-dimensional integrals.A variety of methods have been derived.MCMC algorithm is one of the methods.The advantage of the MCMC algorithm is that it is not affected by the dimension,and its estimation parameters are based on the real likelihood function to ensure the accuracy of the estimation results.Since the MCMC algorithm is easy to implement,this method is also applied to the parameter estimation of the SV model.The modeling application of high-frequency financial data in hours,minutes and even seconds is more and more extensive.Therefore,how to balance accuracy and convergence speed is a problem to be solved in estimating problems.Therefore,the traditional MCMC algorithm needs to be improved.For improving the MCMC algorithm,there are usually two ways to do it.One is to transform the state space of the model by filtering,and the spatial auto-correlation can be reduced by spatial transformation,thereby improving the computational efficiency of the MCMC method.The other is to improve the sampling of the MCMC algorithm itself,such as speeding up the sampling speed and improving the sampling method.This paper focuses on the MCMC algorithm and introduces an easy-to-implement MCMC algorithm(parallelising Markov chain Monte Carlo)algorithm.This paper combines the wavelet filter with the parallel MCMC algorithm to estimate the parameters of the SV model.The advantage of the parallel MCMC algorithm is that it adopts different parallelization mechanisms for different property parameters,directly optimizes the sampling process,and can be easily programmed.In this paper,the wavelet filter and the parallel MCMC algorithm are used to estimate the SV model parameters.The db wavelet filter can filter the high-frequency noise in the financial data and preserve the part containing the real information.The filtered signal reduces the autocorrelation and can reduce the sampling time of the MCMC algorithm to some extent.This paper selects the data of the Shanghai Composite Index from January 4,2010 to December 28,2018,and uses the traditional MCMC algorithm and the parallel MCMC algorithm to estimate the SV model parameters.The two types of methods are compared by comparing the convergence of the estimated parameters,the estimation results of the parameters and the estimation accuracy,and the simulation iteration speed.The empirical results show that after the wavelet filter is processed,the stock return rate sequence is more obvious than the pre-denoising fluctuation law.The parallel MCMC algorithm is used to estimate the model parameters.The parallel MCMC algorithm estimates are consistent with the traditional MCMC algorithm.Both of them have high precision,and in the operation speed,the parallel MCMC algorithm is several times faster than the traditional MCMC algorithm,and its acceleration efficiency is related to the structure of the model,the amount of data,and the number of Markov chains.