IDEAS home Printed from https://ideas.repec.org/p/hst/ghsdps/gd12-264.html
   My bibliography  Save this paper

Investigating Impacts of Self-Exciting Jumps in Returns and Volatility: A Bayesian Learning Approach

Author

Listed:
  • Andras Fulop
  • Junye Li
  • Jun Yu

Abstract

The paper proposes a new class of continuous-time asset pricing models where whenever there is a negative jump in asset returns, it is simultaneously passed on to diffusion variance and the jump intensity, generating co-jumps of prices and volatility and jump clustering. To properly deal with parameter uncertainty and hindsight bias, we employ a Bayesian learning approach, which generates all quantities necessary for sequential real-time model analysis. Empirical study 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 weak evidence of jump clustering. Learning and parameter uncertainty are shown to have important implications for risk management, option pricing and volatility forecasting.

Suggested Citation

  • Andras Fulop & Junye Li & Jun Yu, 2012. "Investigating Impacts of Self-Exciting Jumps in Returns and Volatility: A Bayesian Learning Approach," Global COE Hi-Stat Discussion Paper Series gd12-264, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd12-264
    as

    Download full text from publisher

    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd12-264.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    2. 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.
    3. Wu, Liuren, 2011. "Variance dynamics: Joint evidence from options and high-frequency returns," Journal of Econometrics, Elsevier, vol. 160(1), pages 280-287, January.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
    7. 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.
    8. Viktor Todorov & George Tauchen, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 356-371, July.
    9. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
    10. Todorov, Viktor, 2011. "Econometric analysis of jump-driven stochastic volatility models," Journal of Econometrics, Elsevier, vol. 160(1), pages 12-21, January.
    11. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    12. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
    13. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    14. 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.
    15. Benzoni, Luca & Collin-Dufresne, Pierre & Goldstein, Robert S., 2011. "Explaining asset pricing puzzles associated with the 1987 market crash," Journal of Financial Economics, Elsevier, vol. 101(3), pages 552-573, September.
    16. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
    17. Todorov, Viktor, 2009. "Estimation of continuous-time stochastic volatility models with jumps using high-frequency data," Journal of Econometrics, Elsevier, vol. 148(2), pages 131-148, February.
    18. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    19. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    20. 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.
    21. 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.
    22. repec:dau:papers:123456789/1392 is not listed on IDEAS
    23. Helyette Geman & P. Carr & D. Madan & M. Yor, 2003. "Stochastic Volatility for Levy Processes," Post-Print halshs-00144385, HAL.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Self-Excitation; Volatility Jump; Jump Clustering; Parameter Learning; Sequential Bayes Factor; Risk Management; Option Pricing; Volatility Forecasting;

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hst:ghsdps:gd12-264. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tatsuji Makino). General contact details of provider: http://edirc.repec.org/data/iehitjp.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.