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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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    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
    3. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2010. "Volatility Dynamics for the S&P500: Evidence from Realized Volatility, Daily Returns, and Option Prices," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 3141-3189, August.
    4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    5. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    7. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    8. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Malik, Sheheryar & Pitt, Michael K., 2011. "Particle filters for continuous likelihood evaluation and maximisation," Journal of Econometrics, Elsevier, vol. 165(2), pages 190-209.
    11. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    12. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    13. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    14. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    15. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    16. Duan, Jin-Chuan & Fulop, Andras, 2009. "Estimating the structural credit risk model when equity prices are contaminated by trading noises," Journal of Econometrics, Elsevier, vol. 150(2), pages 288-296, June.
    17. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    18. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    3. Lux, Thomas, 2022. "Inference for Nonlinear State Space Models: A Comparison of Different Methods applied to Markov-Switching Multifractal Models," Econometrics and Statistics, Elsevier, vol. 21(C), pages 69-95.
    4. 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.
    5. 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).
    6. Yonekura, Shouto & Beskos, Alexandros & Singh, Sumeetpal S., 2021. "Asymptotic analysis of model selection criteria for general hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 164-191.
    7. Robert Stok & Paul Bilokon, 2023. "From Deep Filtering to Deep Econometrics," Papers 2311.06256, arXiv.org.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Mumtaz, Haroon, 2018. "A generalised stochastic volatility in mean VAR," Economics Letters, Elsevier, vol. 173(C), pages 10-14.
    15. Haroon Mumtaz, 2018. "A generalised stochastic volatility in mean VAR," Working Papers 855, Queen Mary University of London, School of Economics and Finance.

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