An Beyesian Estimation Of Heston Model With Markov-Switching

In the research of Black-Scholes Model, Heston model presented by Heston(1993) works well among long trends of the volatility process in assets price process.While Hamilton presented Markov-Switching model in 1989, which was proposed to describe the shifts of the parameters in Mathematical models between occasional economic phenomena and rouse many interests among the researchers. This paper combines Heston stochastic volatility model and Markov-Switching model to construct a now model called Markov-Switching-Heston model, which takes both advantages of these two models to simulate the stochastic process of assets price.In this paper, we try to add Markov-Switching process to Heston stochastic volatility process and make a few discuss about the new model. The main work is using a Markov Chain Monte Carlo(MCMC) approach for Beyesian estimation of a discrete time Markov-Switching Heston model to estimate the parameters of the model,including Gibbs sampling combined with Metropolis-Hastings algorithm. We use both Monte Carlo and Quasi-Monte Carlo sequences to construct the Markov chain in the algorithm and compare the result of these two methods.In the paper we make the simulation with Ms-Heston model and the estimation of the parameters. We conjecture that MCMC algorithm is precise and efficient in the estimation of the parameters in MS-Heston model. We also conjecture that using Quasi-Monte Carlo sequences can reduce the variance of the results of estimation,which improves the standard MCMC algorithm.