基于极差的区制转移随机波动率模型及其应用

Range based regime switching stochastic volatility models with applications

关于金融波动率的建模,大量文献都是基于将收益率作为波动率代理变量,而基于极差这一更有效的代理变量研究波动率的则相对较少.考虑到随机波动率模型的优势,将区制转移引入到基于极差的随机波动率模型中,从而刻画金融市场中波动率水平可能存在的结构变化.随后给出此波动率模型的MCMC估计,并利用模拟证明了该方法的有效性.基于以上模型,对上证综指、深圳成指和沪深300指数的极差波动率进行了实证研究,并利用已实现波动率作为基准、以稳健的损失函数作为判断准则的比较方法,与文献中常用的GARCH类模型和SV类模型进行比较,进一步论证了提出模型的优势.

For financial volatility modeling, most of the studies use returns as proxies of volatility, whereas very few are devoted to volatility methods based on range, which is a more efficient proxy. Taking the advantages of stochastic volatility method into consideration, this paper introduces the regime shifts of volatility levels into the range based stochastic volatility model to capture possible structural changes in volatility levels in financial markets. Afterwards, this paper describes the MCMC algorithm to estimate the model and demonstrates its efficiency through a simulation. In the empirical part, based on the range data of Shanghai Composite Index, Shenzhen Component Index and China Securities Index 300, the RMSSV model is estimated. Using the realized volatility as the benchmark and robust loss function as the criterion, the relative advantage of the RMSSV model in comparison with several popular models in GARCH and SV families is demonstrated.