关键词: 随机波动率, 门限效应, 非对称性, 已实现波动率, 有效重要性抽样

Abstract: Volatility in financial markets has attracted a great deal of attention from academics, policy makers and practitioners during the past decades, primarily because it plays a crucial role in many financial applications, such as portfolio selection, option pricing and risk management. It has been well-documented in the finance literature that the financial market volatility is not a constant but in fact changes over time and financial time series exhibits volatility clustering. In addition, many empirical researches have indicated that the mean and volatility of asset returns respond asymmetrically to market news. Recently, with the development of information technology, the availability of high frequency data means that it has become possible to measure the latent volatility using the so-called realized volatility (RV) measure. Under some assumptions, the RV is a consistent estimator of the true volatility. In the real market, however, the RV measure computed from high frequency return data suffers from microstructure noise. In this paper, both the threshold effects and realized volatility measure are incorporated into the standard stochastic volatility (SV) model and the threshold realized SV (TRSV) model is proposed to model the volatility of asset returns. The model is able to account for time-varying volatility and volatility clustering and capture simultaneously the mean and volatility asymmetries in asset return data. Also, this model, which uses high-frequency data containing valuable intraday information to extract volatility information, can estimate RV biases and parameters simultaneously. The lack of a closed-form expression of the likelihood function makes the estimation of the SV models being a challenging topic in the literature. In this paper, the efficient importance sampling (EIS) technique is adopted to implement the maximum likelihood (ML) estimation method for our proposed TRSV model. The Monte Carlo simulation study shows that the EIS-ML estimation method can provide appropriate and accurate inference for the parameters of the proposed model. Finally, the TRSV model is applied to the intraday high-frequency data of Shanghai Stock Exchange composite index and Shenzhen Stock Exchange component index of China. Empirical results show that the TRSV model captures the volatility dynamics appropriately and provides better fit to the data compared to the realized SV (RSV) model. Moreover, strong evidence of high persistence of volatility and the mean and volatility asymmetries is detected in Chinese stock markets.

Key words: stochastic volatility, threshold effect, asymmetries, realized volatility, efficient importance sampling