基于EIS的杠杆随机波动率模型的极大似然估计

EIS-based maximum likelihood estimation of stochastic volatility model with leverage effect

杠杆随机波动率(SV-L)模型在金融计量学文献中已经引起了广泛的关注,然而,它的参数估计一直是一个难点.本文基于有效重要性抽样(EIS)技巧,给出了SV-L模型的极大似然(ML)估计方法.为了检验提出的EIS-ML方法的精确性以及小样本性质,构建了蒙特卡罗(MC)模拟实验.结果表明,EIS-ML方法是非常准确和有效的.最后,将EIS-ML方法应用于实际数据,选取上证和深证综合指数的日对数收益率数据为研究样本,利用SV-L模型对中国股市进行了实证分析.结果表明,中国股市具有很强的波动持续性,并且存在显著的杠杆效应.

The stochastic volatility model with a leverage effect （SV-L） has received a great deal of attention in the financial econometrics literature. However, estimation of the SV-L model poses difficulties. In this pa- per, we develop a method for maximum likelihood （ML） estimation of the SV-L model based on the efficient importance sampling （EIS） technique. Monte Carlo （MC） simulations are presented to examine the accuracy and small sample properties of our proposed method. The experimental results show that the EIS-ML method performs very well. Finally, the EIS-ML method is illustrated with real data. We apply the EIS-ML method of SV-L model to the daily log returns of SSE and SZSE Component Index. Empirical results show that a high persistence of volatility and a significant leverage effect exist in China stock market.