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Option pricing with asymmetric heteroskedastic normal mixture models

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  • 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)

Abstract

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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Bibliographic Info

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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Keywords: asymmetric heteroskadastic models; finite mixture models; option pricing; out-of- sample prediction; statistical fit;

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  1. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599.
  2. 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.
  3. James D. Hamilton & Daniel F. Waggoner & Tao Zha, 2004. "Normalization in econometrics," Working Paper 2004-13, Federal Reserve Bank of Atlanta.
  4. 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.
  5. Peter Christoffersen & Steve Heston & Kris Jacobs, 2003. "Option Valuation with Conditional Skewness," CIRANO Working Papers 2003s-50, CIRANO.
  6. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
  7. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2002. "Mixed normal conditional heteroskedasticity," CFS Working Paper Series 2002/10, Center for Financial Studies (CFS).
  8. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
  9. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
  10. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
  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. 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.
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Cited by:
  1. Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Multivariate Option Pricing with Time Varying Volatility and Correlations," Cahiers de recherche 1020, CIRPEE.
  2. Jeroen V.K. Rombouts & Lars Stentoft, 2009. "Bayesian Option Pricing Using Mixed Normal Heteroskedasticity Models," Cahiers de recherche 0926, CIRPEE.
  3. Lars Stentoft, 2011. "What we can learn from pricing 139,879 Individual Stock Options," CREATES Research Papers 2011-52, School of Economics and Management, University of Aarhus.
  4. NESTEROV, Yurii, 2011. "Random gradient-free minimization of convex functions," CORE Discussion Papers 2011001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976, arXiv.org, revised Dec 2013.

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