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ABC of SV: Limited Information Likelihood Inference in Stochastic Volatility Jump-Diffusion Models

Author

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  • Michael Creel

    (Universitat Autònoma de Barcelona and MOVE)

  • Dennis Kristensen

    (University College London, CeMMaP, and CREATES)

Abstract
We develop novel methods for estimation and filtering of continuous-time models with stochastic volatility and jumps using so-called Approximate Bayesian Computation which build likelihoods based on limited information. The proposed estimators and filters are computationally attractive relative to standard likelihood-based versions since they rely on low-dimensional auxiliary statistics and so avoid computation of high-dimensional integrals. Despite their computational simplicity, we find that estimators and filters perform well in practice and lead to precise estimates of model parameters and latent variables. We show how the methods can incorporate intra-daily information to improve on the estimation and filtering. In particular, the availability of realized volatility measures help us in learning about parameters and latent states. The method is employed in the estimation of a flexible stochastic volatility model for the dynamics of the S&P 500 equity index. We find evidence of the presence of a dynamic jump rate and in favor of a structural break in parameters at the time of the recent financial crisis. We find evidence that possible measurement error in log price is small and has little effect on parameter estimates. Smoothing shows that, recently, volatility and the jump rate have returned to the low levels of 2004-2006.

Suggested Citation

  • Michael Creel & Dennis Kristensen, 2014. "ABC of SV: Limited Information Likelihood Inference in Stochastic Volatility Jump-Diffusion Models," CREATES Research Papers 2014-30, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2014-30
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    References listed on IDEAS

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    Cited by:

    1. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(4), pages 861-916, August.
    2. Michael Creel, 2021. "Inference Using Simulated Neural Moments," Econometrics, MDPI, vol. 9(4), pages 1-15, September.
    3. Jan Posp'iv{s}il & Tom'av{s} Sobotka & Philipp Ziegler, 2019. "Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure," Papers 1912.06709, arXiv.org.
    4. Chaya Weerasinghe & Ruben Loaiza-Maya & Gael M. Martin & David T. Frazier, 2023. "ABC-based Forecasting in State Space Models," Monash Econometrics and Business Statistics Working Papers 12/23, Monash University, Department of Econometrics and Business Statistics.
    5. Michael Creel, 2016. "A Note on Julia and MPI, with Code Examples," Computational Economics, Springer;Society for Computational Economics, vol. 48(3), pages 535-546, October.
    6. David T. Frazier & Ruben Loaiza-Maya & Gael M. Martin, 2021. "Variational Bayes in State Space Models: Inferential and Predictive Accuracy," Papers 2106.12262, arXiv.org, revised Feb 2022.
    7. Creel, Michael, 2017. "Neural nets for indirect inference," Econometrics and Statistics, Elsevier, vol. 2(C), pages 36-49.
    8. D T Frazier & G M Martin & C P Robert & J Rousseau, 2018. "Asymptotic properties of approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 105(3), pages 593-607.
    9. Jan Pospíšil & Tomáš Sobotka & Philipp Ziegler, 2019. "Robustness and sensitivity analyses for stochastic volatility models under uncertain data structure," Empirical Economics, Springer, vol. 57(6), pages 1935-1958, December.
    10. Creel, Michael & Kristensen, Dennis, 2016. "On selection of statistics for approximate Bayesian computing (or the method of simulated moments)," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 99-114.
    11. Gael M. Martin & Brendan P.M. McCabe & David T. Frazier & Worapree Maneesoonthorn & Christian P. Robert, 2016. "Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 09/16, Monash University, Department of Econometrics and Business Statistics.
    12. Hsiang-Hsi Liu & Yu-Cheng Lin, 2021. "Relationships among US S&P500 Stock Index, its Futures and NASDAQ Index Futures with Volatility Spillover and Jump Diffusion: Modeling and Hedging Performance," Bulletin of Applied Economics, Risk Market Journals, vol. 8(1), pages 121-148.
    13. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    14. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    15. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    16. Gael M. Martin & Brendan P.M. McCabe & Worapree Maneesoonthorn & Christian P. Robert, 2014. "Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 20/14, Monash University, Department of Econometrics and Business Statistics.
    17. David T. Frazier & Gael M. Martin & Christian P. Robert, 2015. "On Consistency of Approximate Bayesian Computation," Monash Econometrics and Business Statistics Working Papers 19/15, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    Approximate Bayesian Computation; continuous-time processes; filtering; indirect inference; jumps; realized volatility; stochastic volatility;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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