Malik, Sheheryar and Pitt, Michael K. (2009) Modelling stochastic volatility with leverage and jumps: a simulated maximum likelihood approach via particle filtering. Working Paper. University of Warwick, Department of Economics, Coventry.

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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.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Financial leverage, Jump processes, Stochastic processes, Markov processes, Monte Carlo method, Stock price indexes
Series Name:	Warwick economic research papers
Publisher:	University of Warwick, Department of Economics
Place of Publication:	Coventry
Date:	3 April 2009
Number:	No.897
Number of Pages:	29
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
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URI:	http://wrap.warwick.ac.uk/id/eprint/1320

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