Modelling stochastic volatility with leverage and jumps: a simulated maximum likelihood approach via particle filtering
Malik, Sheheryar and Pitt, Michael K. (2009) Modelling stochastic volatility with leverage and jumps: a simulated maximum likelihood approach via particle filtering. Working Paper. Coventry: University of Warwick, Department of Economics. Warwick economic research papers (No.897).
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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|
|Official Date:||3 April 2009|
|Number of Pages:||29|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
Bates, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in
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