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Modelling stochastic volatility with leverage and jumps: a\ud simulated maximum likelihood approach via particle filtering

By Sheheryar Malik and Michael K. Pitt

Abstract

In this paper we provide a unified methodology in order to conduct likelihood-based inference on the unknown parameters of a general class of discrete-time stochastic volatility models, characterized by both a leverage effect and jumps in returns. Given the non-linear/non-Gaussian state-space form, approximating the likelihood for the parameters is conducted with output generated by the particle filter. Methods are employed to ensure that the approximating likelihood is continuous as a function of the unknown parameters thus enabling the use of Newton-Raphson type maximization algorithms. Our approach is robust and efficient relative to alternative Markov Chain Monte Carlo schemes employed in such contexts. In addition it provides a feasible basis for undertaking the non-trivial task of model comparison. The technique is applied to daily returns data for various stock price indices. We find strong evidence in favour of a leverage effect in all cases. Jumps are an important component in two out of the four series we consider

Topics: HB
Publisher: University of Warwick, Department of Economics
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:1320

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