IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options

  • Peter Christoffersen
  • Kris Jacobs
  • Chayawat Ornthanalai

Standard empirical investigations of jump dynamics in returns and volatility are fairly complicated due to the presence of latent continuous-time factors. We present a new discrete-time framework that combines heteroskedastic processes with rich specifications of jumps in returns and volatility. Our models can be estimated with ease using standard maximum likelihood techniques. We provide a tractable risk neutralization framework for this class of models which allows for separate modeling of risk premia for the jump and normal innovations. We anchor our models in the literature by providing continuous time limits of the models. The models are evaluated by fitting a long sample of S&P500 index returns, and by valuing a large sample of options. We find strong empirical support for time-varying jump intensities. A model with jump intensity that is affine in the conditional variance performs particularly well both in return fitting and option valuation. Our implementation allows for multiple jumps per day, and the data indicate support for this model feature, most notably on Black Monday in October 1987. Our results also confirm the importance of jump risk premia for option valuation: jumps cannot significantly improve the performance of option pricing models unless sizeable jump risk premia are present. Les recherches empiriques standards portant sur la dynamique des sauts dans les rendements et dans la volatilité sont plutôt complexes en raison de la présence de facteurs inobservables en temps continu. Nous présentons un nouveau cadre d'étude en temps discret qui combine des processus hétéroscédastiques et des caractéristiques à concentration élevée de sauts dans les rendements et dans la volatilité. Nos modèles peuvent être facilement évalués à l'aide des méthodes standards du maximum de vraisemblance. Nous offrons une démarche souple de neutralisation du risque pour cette catégorie de modèles, ce qui permet de modéliser distinctement les primes de risque liées aux sauts et celles liées aux innovations normales. Nous imbriquons nos modèles dans la littérature en établissant leurs limites en temps continu. Ces derniers sont évalués en intégrant un échantillon de rendements à long terme de l'indice S&P 500 et en évaluant un vaste échantillon d'options. Nous trouvons un solide appui empirique en ce qui a trait aux intensités de sauts variant dans le temps. Un modèle avec intensité de saut affine dans la variance conditionnelle est particulièrement efficace sur les plans de l'ajustement des rendements et de l'évaluation des options. La mise en uvre de notre modèle permet de multiples sauts par jour et les données appuient cette caractéristique, plus particulièrement en ce qui a trait au lundi noir d'octobre 1987. Nos résultats confirment aussi l'importance des primes liées au risque de sauts pour l'évaluation du prix des options : les sauts ne peuvent contribuer à améliorer considérablement la performance des modèles utilisés pour fixer les prix des options, sauf en présence de primes de risque de sauts assez importantes.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.cirano.qc.ca/files/publications/2009s-34.pdf
Download Restriction: no

Paper provided by CIRANO in its series CIRANO Working Papers with number 2009s-34.

as
in new window

Length: 58 pages
Date of creation: 01 Aug 2009
Date of revision:
Handle: RePEc:cir:cirwor:2009s-34
Contact details of provider: Postal: 1130 rue Sherbrooke Ouest, suite 1400, Montréal, Quéc, H3A 2M8
Phone: (514) 985-4000
Fax: (514) 985-4039
Web page: http://www.cirano.qc.ca/
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Jing-zhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time-Changed Lévy Processes," Journal of Finance, American Finance Association, vol. 59(3), pages 1405-1440, 06.
  2. John M. Maheu & Thomas H. McCurdy, 2003. "News Arrival, Jump Dynamics and Volatility Components for Individual Stock Returns," CIRANO Working Papers 2003s-38, CIRANO.
  3. Fernandez, Pablo, 2006. "Equity premium: Historical, expected, required and implied," IESE Research Papers D/661, IESE Business School.
  4. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December.
  5. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
  6. Ivo Welch, 2000. "Views of Financial Economists on the Equity Premium and on Professional Controversies," Yale School of Management Working Papers ysm122, Yale School of Management.
  7. Jeremy J. Siegel & Richard H. Thaler, 1997. "Anomalies: The Equity Premium Puzzle," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 191-200, Winter.
  8. 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.
  9. 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.
  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. John M Maheu & Thomas H McCurdy, 2007. "Modeling foreign exchange rates with jumps," Working Papers tecipa-279, University of Toronto, Department of Economics.
  13. 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.
  14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  15. 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.
  16. 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, 06.
  17. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.
  18. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
  19. 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.
  20. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
  21. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
  22. 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.
  23. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-778, 04.
  24. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
  25. Mehra, Rajnish & Prescott, Edward C., 2003. "The equity premium in retrospect," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 14, pages 889-938 Elsevier.
  26. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
  27. 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.
  28. John H Cochrane, 2003. "Where is the Market Going: Uncertain Facts and Novel Theories," Levine's Working Paper Archive 618897000000000762, David K. Levine.
  29. Jeff Fleming & Chris Kirby, 2003. "A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 365-419.
  30. David S. Bates, 2006. "Maximum Likelihood Estimation of Latent Affine Processes," Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 909-965.
  31. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
  32. 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.
  33. Giovanni Barone-Adesi & Robert F. Engle & Loriano Mancini, 2008. "A GARCH Option Pricing Model with Filtered Historical Simulation," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1223-1258, May.
  34. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:cir:cirwor:2009s-34. 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: (Webmaster)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.