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What we can learn from pricing 139,879 Individual Stock Options

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  • Lars Stentoft

    ()
    (HEC Montréal, CIRANO, CIRPEÉ, and CREATES)

Abstract

The GARCH framework has been used for option pricing with quite some success. While the initial work assumed conditional Gaussian innovations, recent contributions relax this assumption and allow for more flexible parametric specifications of the underlying distribution. However, until now the empirical applications have been limited to index options or options on only a few stocks and this using only few potential distributions and variance specififications. In this paper we test the GARCH framework on 30 stocks in the Dow Jones Industrial Average using two classical volatility specififications and 7 different underlying distributions. Our results provide clear support for using an asymmetric volatility specifification together with non-Gaussian distribution, particularly of the Normal Inverse Gaussian type, and statistical tests show that this model is most frequently among the set of best performing models.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-52.

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Length: 54
Date of creation: 21 Dec 2011
Date of revision:
Handle: RePEc:aah:create:2011-52

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Web page: http://www.econ.au.dk/afn/

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Keywords: American options; GARCH models; Model Confidence Set; Simulation.;

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  1. Lehar, Alfred & Scheicher, Martin & Schittenkopf, Christian, 2002. "GARCH vs. stochastic volatility: Option pricing and risk management," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 323-345, March.
  2. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
  3. HÄRDLE, Wolfgang & HAFNER, Christian, 1997. "Discrete time option pricing with flexible volatility estimation," CORE Discussion Papers 1997047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  5. Jeroen V.K. Rombouts & Lars Stentoft, 2010. "Option Pricing with Asymmetric Heteroskedastic Normal Mixture Models," CREATES Research Papers 2010-44, School of Economics and Management, University of Aarhus.
  6. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 10.
  7. Lars Stentoft, 2008. "American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution," CREATES Research Papers 2008-41, School of Economics and Management, University of Aarhus.
  8. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
  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. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
  11. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
  12. 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.
  13. Duan, Jin-Chuan & Zhang, Hua, 2001. "Pricing Hang Seng Index options around the Asian financial crisis - A GARCH approach," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 1989-2014, November.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
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