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

1. 在随机波动率模型的MCMC（马尔可夫链蒙特卡罗）贝叶斯分析中，我们必须从其后验分布中抽取潜在波动率的样本。对波动率进行采样的一种有效方法是Shephard和Pitt（1997）提出的多步采样器。我们还开发了MCMC贝叶斯方法来分析扩展的随机波动模型，如非正态误差随机波动模型、马尔可夫切换随机波动模型和动态二元混合模型。我们还开发了MCMC贝叶斯方法来分析GARCH模型。该方法使我们能够预测未来的波动率，并考虑GARCH参数的估计误差来评估期权价格。日本股票市场的实证分析随机波动率模型通常假设资产收益以潜在波动率为条件的分布是正态分布。我们证明t分布比正态分布和其他分布如GED和正态混合更适合东证指数。我们还表明，使用TOPDL的周收益，允许波动率均值移动的马尔可夫切换模型比标准随机波动率模型更受欢迎。我们还表明，Thuchen和Pitts（1983）和Andersen（1996）提出的动态二元混合模型不能完全解释日经225股指期货市场的价格和交易量行为3。基于波动率变化模型的期权价格评估我们开发了一种MCMC贝叶斯方法来评估标的资产价格遵循GARCH模型时的期权价格，并表明该方法在日经225指数期权价格的评估中表现良好。

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.