Lévy过程驱动的非高斯OU随机波动模型及其贝叶斯参数统计推断方法研究

本文采用CGMY和GIG过程对非高斯OU随机波动率模型进行扩展,建立连续叠加Lévy过程驱动的非高斯OU随机波动率模型,并给出模型的散粒噪声(Shot-Noise)表现方式与近似。在此基础上,为了反映的波动率相关性,本文把回顾抽样(Retrospective Sampling)方法扩展到连续叠加的Lévy过程驱动的非高斯OU随机波动模型中,设计了Lévy过程驱动的非高斯OU随机波动模型的贝叶斯参数统计推断方法。最后,采用金融市场实际数据对不同模型和参数估计方法进行验证和比较研究。本文理论和实证研究均表明采用CGMY和GIG过程对非高斯OU随机波动率模型进行扩展之后,模型的绩效得到明显提高,更能反映金融资产收益率波动率变化特征,本文设计的Lévy过程驱动的非高斯OU随机波动模型的贝叶斯参数统计推断方法效率也较高,克服了已有研究的不足。同时,实证研究发现上证指数收益率和波动率跳跃的特征以及波动率序列具有明显的长记忆特性。

The Non Ornstein-Uhlenbeck Models Driven by the General Lévy Process and Its Bayesian Inference

The currently most popular models for the volatility of financial time series, non Gaussian Ornstein-Uhlenbeck stochastic processes are extended to more general non Ornstein-Uhlenbeck models driven by the general Lévy process, such as Generalized Inverse Gaussian(GIG)and Tempered Stable distributions(CGMY). In particular, means of making the correlation structure in the volatility process more flexible based on continuous superpositions of the more general non Ornstein-Uhlenbeck models are investigated, which can introduce long-memory into the volatility model. A shot-noise process and approximation for the continuous superpositions process are represented. Inference is carried out in a Bayesian framework, with computation using extended Reversible Jump Markov chain Monte Carlo and dependent thinning to the continuous superposition case. Empirical research demonstrates that the efficient Markov chain Monte Carlo methods appear to be successful in the case of the general GIG and CGMY marginal model, and that those models can be fitted to real share price returns data, and that results indicate that for the series we study, the long-memory aspect of the model is supported.