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Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility

Author

Listed:
  • Andras Fulop

    (Finance Department, ESSEC Business School, Paris-Singapore, Cergy-Pontoise Cedex, France 95021)

  • Junye Li

    (Finance Department, ESSEC Business School, Paris-Singapore, 100 Victoria Street, Singapore 188064)

  • Jun Yu

    (Sim Kee Boon Institute for Financial Economics, School of Economics, and Lee Kong Chian School of Business, Singapore Management University, 90 Stamford Road, Singapore 178903)

Abstract
The paper proposes a new class of continuous-time asset pricing models where negative jumps play a crucial role. Whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating self-exciting co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and in-sample over-fitting, a Bayesian learning approach combined with an efficient particle filter is employed. It not only allows for comparison of both nested and non-nested models, but also generates all quantities necessary for sequential model analysis. Empirical investigation using S&P 500 index returns shows that volatility jumps at the same time as negative jumps in asset returns mainly through jumps in diffusion volatility. We find substantial evidence for jump clustering, in particular, after the recent financial crisis in 2008, even though parameters driving dynamics of the jump intensity remain difficult to identify.

Suggested Citation

  • Andras Fulop & Junye Li & Jun Yu, 2012. "Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility," Working Papers 03-2012, Singapore Management University, School of Economics.
    • Handle: RePEc:siu:wpaper:03-2012
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    File URL: https://mercury.smu.edu.sg/rsrchpubupload/19790/Self_Exciting.pdf
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    References listed on IDEAS

    as
    1. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    2. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    3. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, October.
    4. Wu, Liuren, 2011. "Variance dynamics: Joint evidence from options and high-frequency returns," Journal of Econometrics, Elsevier, vol. 160(1), pages 280-287, January.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Neil Shephard & Thomas Flury, 2009. "Learning and filtering via simulation: smoothly jittered particle filters," Economics Series Working Papers 469, University of Oxford, Department of Economics.
    7. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
    8. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, October.
    9. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    10. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    11. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    12. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    13. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, October.
    14. Walter R. Gilks & Carlo Berzuini, 2001. "Following a moving target—Monte Carlo inference for dynamic Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 127-146.
    15. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    16. repec:bla:jfinan:v:59:y:2004:i:3:p:1367-1404 is not listed on IDEAS
    17. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    18. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, October.
    19. repec:dau:papers:123456789/1392 is not listed on IDEAS
    20. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Self-Excitation; Volatility Jump; Jump Clustering; Extreme Events; Parameter Learning; Particle Filters; Sequential Bayes Factor; Risk Management;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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