Risk Measures under a Stochastic Volatility Model with a Mixture-of-Normal Error Distribution

Posted: 2 Apr 2013

See all articles by Dinghai Xu

Dinghai Xu

Independent

Tony S. Wirjanto

University of Waterloo - School of Accounting and Finance; University of Waterloo, Department of Statistics & Actuarial Science

Date Written: March 1, 2013

Abstract

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

Suggested Citation

Xu, Dinghai and Wirjanto, Tony S., Risk Measures under a Stochastic Volatility Model with a Mixture-of-Normal Error Distribution (March 1, 2013). Available at SSRN: https://ssrn.com/abstract=2242891

Dinghai Xu

Independent ( email )

Tony S. Wirjanto (Contact Author)

University of Waterloo - School of Accounting and Finance ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)

HOME PAGE: http://https://uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

University of Waterloo, Department of Statistics & Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Canada
519-888-4567 x35210 (Phone)
519-746-1875 (Fax)

HOME PAGE: http://math.uwaterloo.ca/statistics-and-actuarial-science/people-profiles/tony-wirjanto

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