Heavy-tailed mixture GARCH volatility modeling and Value-at-Risk estimation

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Nikolaev, Nikolay; Boshnakov, Georgi N. and Zimmer, Robert. 2013. Heavy-tailed mixture GARCH volatility modeling and Value-at-Risk estimation. Expert Systems with Applications, 40(6), pp. 2233-2243. ISSN 0957-4174 [Article]

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Abstract or Description

This paper presents a heavy-tailed mixture model for describing time-varying conditional distributions in time series of returns on prices. Student-t component distributions are taken to capture the heavy tails typically encountered in such financial data. We design a mixture MT(m)-GARCH(p, q) volatility model for returns, and develop an EM algorithm for maximum likelihood estimation of its parameters. This includes formulation of proper temporal derivatives for the volatility parameters. The experiments with a low order MT(2)-GARCH(1, 1) show that it yields results with improved statistical characteristics and economic performance compared to linear and nonlinear heavy-tail GARCH, as well as normal mixture GARCH. We demonstrate that our model leads to reliable Value-at-Risk performance in short and long trading positions across different confidence levels.

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Article

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https://doi.org/10.1016/j.eswa.2012.10.038