一类金融半参数随机波动模型：贝叶斯分析及其应用

Stochastic volatility model is an important tool for studying financial asset returns, currently is an important direction in the research areas of financial econometrics and statistics. Although the existing stochastic volatility model can better model the phenomenon of volatility clustering and volatility asymmetry, but can not effectively describe the characteristics of leptokurtosis, fat-tail and skewness of conditional distribution. Accurately determining the form of conditional distribution is an important problem in the areas of financial econometrics and statistics, also is the base for establishing reasonable risk measurement models and so on. However, most current literatures focus on parametric conditional distribution, but few literatures focus on nonparametric conditional distribution. Therefore, this project proposes to use stochastic volatility model and nonparametric distribution to build semiparametric stochastic volatility model, and use Bayesian method to study parameter estimation and model selection. Due to the complicated model structure, this project proposes to use the ideas of the random blocking, the retrospective MCMC sampling, the slice sampling, the data augmentation and so on to deal with the problem of parameter estimation. Also we use the robust DIC (RDIC) to study the problem of model selection, and design an effective algorithm for calculating RDIC. Lastly using China financial market data, we compare the practical effects of parametric and semiparametric stochastic volatility models.

随机波动模型是研究金融资产收益的重要工具，目前是国际上计量经济学和统计学研究领域的一个重要方向。尽管现有随机波动模型能够较好地刻画波动的集聚性和非对称性，但未能有效地刻画收益的条件分布特性：尖峰厚尾和偏斜。准确确定收益的条件分布形式是计量经济学界和统计学界一贯关注的问题，也是进一步建立合理风险度量模型等的基础。然而已有文献多集中于参数化条件分布，而对于非参数化条件分布的研究尚不多见。本项目拟在非参数分布和随机波动模型基础上建立半参数随机波动模型，并运用贝叶斯方法对模型进行分析，包括参数估计和模型选择。由于模型结构复杂，本项目拟利用随机分块、回溯MCMC抽样、切片抽样和数据扩充等思想处理参数估计问题；另外利用稳健偏差信息准则（RDIC）研究模型比较问题，并设计RDIC的有效计算方法；最后利用中国金融市场数据对参数和半参数随机波动模型的实际效果进行比较研究。

随机波动模型是研究金融资产收益的重要工具，目前是国际上计量经济学和统计学研究领域的一个重要方向。尽管现有随机波动模型能够较好地刻画波动的集聚性和非对称性，但未能有效地刻画收益的条件分布特性：尖峰厚尾和偏斜。准确确定收益的条件分布形式是计量经济学界和统计学界一贯关注的问题，也是进一步建立合理风险度量模型等的基础。然而已有文献多集中于参数化条件分布，而对于非参数化条件分布的研究尚不多见。本项目拟在非参数分布和随机波动模型基础上建立半参数随机波动模型，并运用贝叶斯方法对模型进行分析，包括参数估计和模型选择。由于模型结构复杂，本项目利用随机分块、回溯MCMC抽样、切片抽样和数据扩充等思想处理了参数估计问题；另外利用稳健偏差信息准则（RDIC）研究了模型比较问题，并设计了RDIC的有效计算方法；最后利用中国金融市场数据对参数和半参数随机波动模型的实际效果进行了比较研究。