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

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Author Info

  • 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)

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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.

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Bibliographic Info

Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 03-2012.

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Length: 44 pages
Date of creation: Jan 2012
Date of revision:
Publication status: Published in SMU Economics and Statistics Working Paper Series
Handle: RePEc:siu:wpaper:03-2012

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Keywords: Self-Excitation; Volatility Jump; Jump Clustering; Extreme Events; Parameter Learning; Particle Filters; Sequential Bayes Factor; Risk Management;

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References

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  1. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
  2. 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.
  3. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
  4. Todorov, Viktor & Tauchen, George, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 356-371.
  5. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
  6. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
  7. Wu, Liuren, 2011. "Variance dynamics: Joint evidence from options and high-frequency returns," Journal of Econometrics, Elsevier, vol. 160(1), pages 280-287, January.
  8. Nicolas Chopin, 2002. "A sequential particle filter method for static models," Biometrika, Biometrika Trust, vol. 89(3), pages 539-552, August.
  9. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
  10. 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.
  11. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  12. Yacine Aït-Sahalia & Julio Cacho-Diaz & Roger J.A. Laeven, 2010. "Modeling Financial Contagion Using Mutually Exciting Jump Processes," NBER Working Papers 15850, National Bureau of Economic Research, Inc.
  13. 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, 06.
  14. 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 327-43.
  15. 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.
  16. Geman, Hélyette & Carr, Peter & Madan, Dilip B. & Yor, Marc, 2003. "Stochastic Volatility for Levy Processes," Economics Papers from University Paris Dauphine 123456789/1392, Paris Dauphine University.
  17. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
  18. 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.
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Cited by:
  1. Worapree Maneesoonthorn & Catherine S. Forbes & Gael M. Martin, 2013. "Inference on Self-Exciting Jumps in Prices and Volatility using High Frequency Measures," Monash Econometrics and Business Statistics Working Papers 28/13, Monash University, Department of Econometrics and Business Statistics.

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