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Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models

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  • Creal, Drew D.

Abstract

Filtering and smoothing algorithms that estimate the integrated variance in Lévy-driven stochastic volatility models are analyzed. Particle filters are algorithms designed for nonlinear, non-Gaussian models while the Kalman filter remains the best linear predictor if the model is linear but non-Gaussian. Monte Carlo experiments are performed to compare these algorithms across different specifications of the model including different marginal distributions and degrees of persistence for the instantaneous variance. The use of realized variance as an observed variable in the state space model is also evaluated. Finally, the particle filter's ability to identify the timing and size of jumps is assessed relative to popular nonparametric estimators.

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  • Creal, Drew D., 2008. "Analysis of filtering and smoothing algorithms for Lévy-driven stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2863-2876, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:2863-2876
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    2. Gong, Xiao-li & Zhuang, Xin-tian, 2016. "Option pricing and hedging for optimized Lévy driven stochastic volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 118-127.
    3. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2017. "Inference on Self‐Exciting Jumps in Prices and Volatility Using High‐Frequency Measures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(3), pages 504-532, April.
    4. Borovkova, Svetlana & Permana, Ferry J., 2009. "Implied volatility in oil markets," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2022-2039, April.
    5. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S., 2020. "High-frequency jump tests: Which test should we use?," Journal of Econometrics, Elsevier, vol. 219(2), pages 478-487.
    6. Worapree Maneesoonthorn & Gael M Martin & Catherine S Forbes, 2018. "Dynamic price jumps: The performance of high frequency tests and measures, and the robustness of inference," Monash Econometrics and Business Statistics Working Papers 17/18, Monash University, Department of Econometrics and Business Statistics.
    7. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    8. Griffin, J.E. & Steel, M.F.J., 2010. "Bayesian inference with stochastic volatility models using continuous superpositions of non-Gaussian Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2594-2608, November.
    9. Pedersen, M.W. & Thygesen, U.H. & Madsen, H., 2011. "Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 280-290, January.
    10. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    11. Kaeck, Andreas & Rodrigues, Paulo & Seeger, Norman J., 2018. "Model Complexity and Out-of-Sample Performance: Evidence from S&P 500 Index Returns," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 1-29.
    12. Worapree Maneesoonthorn & Gael M. Martin & Catherine S. Forbes, 2017. "Dynamic asset price jumps and the performance of high frequency tests and measures," Monash Econometrics and Business Statistics Working Papers 14/17, Monash University, Department of Econometrics and Business Statistics.
    13. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342, June.

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