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

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  • Malik, Sheheryar

    (Department of Economics, University of Warwick,)

  • Pitt, Michael K

    (Department of Economics, University of Warwick,)

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.

Suggested Citation

  • 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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    Cited by:

    1. Davide Raggi & Silvano Bordignon, 2011. "Volatility, Jumps, and Predictability of Returns: A Sequential Analysis," Econometric Reviews, Taylor & Francis Journals, vol. 30(6), pages 669-695.
    2. Jiawen Xu & Pierre Perron, 2015. "Forecasting in the presence of in and out of sample breaks," Boston University - Department of Economics - Working Papers Series wp2015-012, Boston University - Department of Economics.
    3. Robert Stok & Paul Bilokon, 2023. "From Deep Filtering to Deep Econometrics," Papers 2311.06256, arXiv.org.

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    More about this item

    Keywords

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