Risk Measures under a Stochastic Volatility Model with a Mixture-of-Normal Error Distribution
Posted: 2 Apr 2013
Date Written: March 1, 2013
This paper constructs Value at Risk (VaR) measures from a stochastic volatility model with a discrete bivariate mixture-of-normal error distribution - henceforth SV-MN. This volatility-gnerating model is able to accommodate many of the salient features of financial asset returns, such as time-varying volatility, volatility clustering, excess skewness and kurtosis in the return distribution. In addition, it is also able to capture the so-called leverage effect prominent in many asset returns in the equity market. Three sets of Monte-Carlo simulations are conducted to assess the performances of the constructed VaR measures relative to those generated from other competing models. The results show that the VaR measures constructed from the SV-MN model perform well under different data generating processes. We also apply our proposed model to S&P 500 and CRSP stock indices. We find that the empirical VaR measures obtained from our SV-MN model also perform very well relative to those generated from other competing models for the sample return data examined in this paper.
Keywords: Value at Risk, Stochastic Volatility, Mixture of Normals, Generalized Method of Moments, Markov Chain Monte Carlo
JEL Classification: C22, C53, G19
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