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


  • Malik, Sheheryar

    (Department of Economics, University of Warwick,)

  • Pitt, Michael K

    (Department of Economics, University of Warwick,)


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.

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  • Malik, Sheheryar & Pitt, Michael K, 2009. "Modelling Stochastic Volatility with Leverage and Jumps : A Simulated Maximum Likelihood Approach via Particle Filtering," The Warwick Economics Research Paper Series (TWERPS) 897, University of Warwick, Department of Economics.
  • Handle: RePEc:wrk:warwec:897

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    Particle filter ; Simulation ; SIR ; State space ; Leverage effect ; Jumps;

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