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Option pricing with asymmetric heteroskedastic normal mixture models

  • ROMBOUTS, Jeroen V. K.

    ()

    (Institute of Applied Economics at HEC Montréal, CIRANO, CIRPEE, Canada; Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • STENTOFT, Lars

    ()

    (Department of Finance at HEC Montréal, CIRANO, CIRPEE, CREATES, Canada)

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%.

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Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2010049.

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Date of creation: 01 Aug 2010
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Handle: RePEc:cor:louvco:2010049
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  1. Peter Christoffersen & Redouane Elkamhi & Bruno Feunou & Kris Jacobs, 2009. "Option Valuation with Conditional Heteroskedasticity and Non-Normality," CREATES Research Papers 2009-33, School of Economics and Management, University of Aarhus.
  2. 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.
  3. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  4. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
  5. 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.
  6. Markus Haas, 2004. "Mixed Normal Conditional Heteroskedasticity," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 211-250.
  7. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Centre de Recherche en Economie et Statistique.
  8. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
  9. Peter Christoffersen & Steve Heston & Kris Jacobs, 2003. "Option Valuation with Conditional Skewness," CIRANO Working Papers 2003s-50, CIRANO.
  10. 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.
  11. 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.
  12. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
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