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

Authors:
Nikolay Y. Nikolaev;Georgi N. Boshnakov;Robert Zimmer
Affiliations:
Department of Computing, Goldsmiths College, University of London, London SE14 6NW, UK;School of Mathematics, University of Manchester, Manchester M13 9PL, UK;Department of Computing, Goldsmiths College, University of London, London SE14 6NW, UK
Venue:
Expert Systems with Applications: An International Journal
Year:
2013

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Abstract

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.