Econometric Analysis of Stock Markets in Japan using Models of Changing Volatility

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1. Development of Models of Changing VolatilityIn a MCMC (Markov Chain Monte Carlo) Bayesian analysis of stochastic volatility models, we must sample the latent volatilities from their posterior distribution.. One efficient method for sampling volatilities is the multi-move sampler proposed by Shephard and Pitt (1997). We showed that their method is incorrect and we proposed a correct multi-move sampler We also developed a MCMC Bayesian method far the analysis of extended stochastic volatility models such as a stochastic volatility model with non-normal errors, a Markov switching stochastic volatility model and a dynamic bivariate mixture model We also develop a MCMC Bayesian method for the analysis of GARCH models. This method enables us to forecast future volatilities and evaluate option prices considering the estimation errors of GARCH parameters.2. EmpiricalAnalysis of Stock Markets in JapanStochastic volatility model usually assume that the distribution of asset returns conditional on the latent volatility is normal We showed that t distribution fits TOPIX better than the normal and other distributions such as the GED and the normal mixture. We also showed that the Markov switching model that allows for a shift in the mean of volatility is favored over the standard stochastic volatility model using weekly returns of the TOPDL We also showed that the dynamic bivariate mixture models proposed by Thuchen and Pitts (1983) and Andersen (1996) cannot fully explain t behavior of prioe and trading volume in the Nikkei 225 stock index futures market3. Option Price Evaluation using Models of Changing VolatilityWe develop a MCMC Bayesian method for evaluating toption price when the price of underlying asset follows a GARCH model and showed that this method performed well in the evaluation of the price of Nikkei 225 option.