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Simulated likelihood inference for stochastic volatility models using continuous particle filtering

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  • Michael Pitt
  • Sheheryar Malik
  • Arnaud Doucet

Abstract

Discrete-time stochastic volatility (SV) models have generated a considerable literature in financial econometrics. However, carrying out inference for these models is a difficult task and often relies on carefully customized Markov chain Monte Carlo techniques. Our contribution here is twofold. First, we propose a new SV model, namely SV–GARCH, which bridges the gap between SV and GARCH models: it has the attractive feature of inheriting unconditional properties similar to the standard GARCH model but being conditionally heavier tailed. Second, we propose a likelihood-based inference technique for a large class of SV models relying on the recently introduced continuous particle filter. The approach is robust and simple to implement. The technique is applied to daily returns data for S&P 500 and Dow Jones stock price indices for various spans. Copyright The Institute of Statistical Mathematics, Tokyo 2014

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  • Michael Pitt & Sheheryar Malik & Arnaud Doucet, 2014. "Simulated likelihood inference for stochastic volatility models using continuous particle filtering," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 527-552, June.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:3:p:527-552
    DOI: 10.1007/s10463-014-0456-y
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    4. Haroon Mumtaz, 2018. "A generalised stochastic volatility in mean VAR," Working Papers 855, Queen Mary University of London, School of Economics and Finance.
    5. Song, Zhaogang & Xiu, Dacheng, 2016. "A tale of two option markets: Pricing kernels and volatility risk," Journal of Econometrics, Elsevier, vol. 190(1), pages 176-196.
    6. Johan Dahlin & Thomas B. Schon, 2015. "Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models," Papers 1511.01707, arXiv.org, revised Mar 2019.
    7. Mao, Xiuping & Czellar, Veronika & Ruiz, Esther & Veiga, Helena, 2020. "Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 13(C), pages 84-105.
    8. Lux, Thomas, 2018. "Estimation of agent-based models using sequential Monte Carlo methods," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 391-408.
    9. Robert Stok & Paul Bilokon, 2023. "From Deep Filtering to Deep Econometrics," Papers 2311.06256, arXiv.org.
    10. Awijen, Haithem & Ben Zaied, Younes & Nguyen, Duc Khuong & Sensoy, Ahmet, 2020. "Endogenous Financial Uncertainty and Macroeconomic Volatility: Evidence from the United States," MPRA Paper 101276, University Library of Munich, Germany, revised Jun 2020.
    11. Mumtaz, Haroon, 2018. "A generalised stochastic volatility in mean VAR," Economics Letters, Elsevier, vol. 173(C), pages 10-14.
    12. Lux, Thomas, 2017. "Estimation of agent-based models using sequential Monte Carlo methods," Economics Working Papers 2017-07, Christian-Albrechts-University of Kiel, Department of Economics.
    13. Zhang, Xing & Yan, Zhibin & Chen, Yunqi & Yuan, Yanhua, 2022. "A novel particle filter for extended target tracking with random hypersurface model," Applied Mathematics and Computation, Elsevier, vol. 425(C).
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    15. Benedikt Rotermann & Bernd Wilfling, 2015. "Estimating rational stock-market bubbles with sequential Monte Carlo methods," CQE Working Papers 4015, Center for Quantitative Economics (CQE), University of Muenster.

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