Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach via Particle Filtering

Sheheryar Malik and Michael K Pitt
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Sheheryar Malik: Department of Economics, University of Warwick,
Michael K Pitt: Department of Economics, University of Warwick,

The Warwick Economics Research Paper Series (TWERPS) from University of Warwick, Department of Economics

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 e®ect 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.

Keywords: Particle filter; Simulation; SIR; State space; Leverage effect; Jumps (search for similar items in EconPapers)
Date: 2009
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:wrk:warwec:897

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