IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

Option Pricing with Asymmetric Heteroskedastic Normal Mixture Models

  • Jeroen Rombouts
  • Lars Peter Stentoft

This paper uses asymmetric heteroskedastic normal mixture models to fit return data and to price options. The models can be estimated straightforwardly by maximum likelihood, have high statistical fit when used on S&P 500 index return data, and allow for substantial negative skewness and time varying higher order moments of the risk neutral distribution. When forecasting out-of-sample a large set of index options between 1996 and 2009, substantial improvements are found compared to several benchmark models in terms of dollar losses and the ability to explain the smirk in implied volatilities. Overall, the dollar root mean squared error of the best performing benchmark component model is 39% larger than for the mixture model. When considering the recent financial crisis this difference increases to 69%. Dans le présent document, nous avons recours aux modèles hétéroscédastiques asymétriques avec mélange de distributions normales pour ajuster les données sur les rendements et fixer les prix des options. Les modèles peuvent être estimés directement par le maximum de vraisemblance, ils comportent un ajustement statistique élevé quand ils sont utilisés sur les données de rendement de l'indice S&P 500, et ils permettent de tenir compte d'une asymétrie négative importante et des moments d'ordre élevé variant dans le temps liés à la distribution du risque nul. Dans le cas des prévisions hors-échantillonnage concernant une vaste gamme d'options sur indice entre 1996 et 2009, nous constatons des améliorations substantielles, par rapport à plusieurs modèles de référence, en termes de pertes exprimées en dollars et de capacité d'expliquer le caractère ironique des volatilités implicites. En général, la racine de l'erreur quadratique moyenne du modèle de référence à composantes le plus efficace est 39 % plus grande que dans le cas du modèle à mélange. Dans le contexte de la récente crise financière, cette différence augmente à 69 %.

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/2010s-38.pdf
Download Restriction: no

Paper provided by CIRANO in its series CIRANO Working Papers with number 2010s-38.

as
in new window

Length: 48 pages
Date of creation: 01 Sep 2010
Date of revision:
Handle: RePEc:cir:cirwor:2010s-38
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. 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.
  2. Jin-Chuan Duan & Peter Ritchken & Zhiqiang Sun, 2006. "Approximating Garch-Jump Models, Jump-Diffusion Processes, And Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 21-52.
  3. Peter Christoffersen & Kris Jacobs & Yintian Wang, 2004. "Option Valuation with Long-run and Short-run Volatility Components," CIRANO Working Papers 2004s-56, CIRANO.
  4. BAUWENS, Luc & HAFNER, Christian & ROMBOUTS, Jeroen, 2006. "Multivariate mixed normal conditional heteroskedasticity," CORE Discussion Papers 2006012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  6. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
  7. ROMBOUTS, Jeroen V.K. & STENTOFT, Lars, 2009. "Bayesian option pricing using mixed normal heteroskedasticity models," CORE Discussion Papers 2009013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. 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.
  9. ROMBOUTS, Jeroen J. K & STENTOFT, Lars, 2010. "Multivariate option pricing with time varying volatility and correlations," CORE Discussion Papers 2010020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  11. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1998. "Pricing and Hedging Long-Term Options," Yale School of Management Working Papers ysm90, Yale School of Management.
  12. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," FRB Atlanta Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  13. BAUWENS, Luc & ROMBOUTS, Jeroen, 2003. "Bayesian clustering of many GARCH models," CORE Discussion Papers 2003087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Bertholon, H. & Monfort, A. & Pegoraro, F., 2007. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working papers 188, Banque de France.
  15. Peter Christoffersen & Steven Heston & Kris Jacobs, 2013. "Capturing Option Anomalies with a Variance-Dependent Pricing Kernel," Review of Financial Studies, Society for Financial Studies, vol. 26(8), pages 1963-2006.
  16. Helyette Geman & P. Carr & D. Madan & M. Yor, 2003. "Stochastic Volatility for Levy Processes," Post-Print halshs-00144385, HAL.
  17. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
  18. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
  19. AMIR, Rabah, . "Supermodularity and complementarity in economics: an elementary survey," CORE Discussion Papers RP 1823, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  20. Peter R. Hansen & Asger Lunde & James M. Nason, 2010. "The Model Confidence Set," CREATES Research Papers 2010-76, Department of Economics and Business Economics, Aarhus University.
  21. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
  22. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  23. Luc Bauwens & Arie Preminger & Jeroen V. K. Rombouts, 2010. "Theory and inference for a Markov switching GARCH model," Econometrics Journal, Royal Economic Society, vol. 13(2), pages 218-244, 07.
  24. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2010. "Option Valuation with Conditional Heteroskedasticity and Nonnormality," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2139-2183.
  25. 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.
  26. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  27. Christoffersen, Peter & Dorion, Christian & Jacobs, Kris & Wang, Yintian, 2010. "Volatility Components, Affine Restrictions, and Nonnormal Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 483-502.
  28. Becker, Ralf & Clements, Adam E., 2008. "Are combination forecasts of S&P 500 volatility statistically superior?," International Journal of Forecasting, Elsevier, vol. 24(1), pages 122-133.
  29. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
  30. 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.
  31. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
  32. repec:dau:papers:123456789/1392 is not listed on IDEAS
  33. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
  34. Bertholon, H. & Monfort, A. & Pegoraro, F., 2008. "Econometric Asset Pricing Modelling," Working papers 223, Banque de France.
  35. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  36. Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, Department of Economics and Business Economics, Aarhus University.
  37. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
  38. BOUADDI, Mohammed & ROMBOUTS, Jeroen V.K., 2007. "Mixed exponential power asymmetric conditional heteroskedasticity," CORE Discussion Papers 2007097, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  39. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
  40. Awartani, Basel M.A. & Corradi, Valentina, 2005. "Predicting the volatility of the S&P-500 stock index via GARCH models: the role of asymmetries," International Journal of Forecasting, Elsevier, vol. 21(1), pages 167-183.
  41. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
  42. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
  43. K. Hsieh & P. Ritchken, 2005. "An empirical comparison of GARCH option pricing models," Review of Derivatives Research, Springer, vol. 8(3), pages 129-150, December.
  44. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
  45. Badescu Alex & Kulperger Reg & Lazar Emese, 2008. "Option Valuation with Normal Mixture GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(2), pages 1-42, May.
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:2010s-38. 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.