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Which pricing approach for options under GARCH with non-normal innovations?

Author

Listed:
  • Jean-Guy Simonato

    () (HEC Montreál)

  • Lars Stentoft

    () (University of Western Ontario and CREATES)

Abstract

Two different pricing frameworks are typically used in the literature when pricing options under GARCH with non-normal innovations: the equilibrium approach and the no-arbitrage approach. Each framework can accommodate various forms of GARCH and innovation distributions, but empirical implementation and tests are typically done in one framework or the other because of the computational challenges that are involved in obtaining the relevant pricing parameters. We contribute to the literature by comparing and documenting the empirical performance of a GARCH specification which can be readily implemented in both pricing frameworks. The model uses a parsimonious GARCH specification with skewed and leptokurtic Johnson Su innovations together with either the equilibrium based framework or the no-arbitrage based framework. Using a large sample of options on the S&P 500 index, we find that the two approaches give rise to very similar pricing errors when implemented with time-varying pricing parameters. However, when implemented with constant pricing parameters, the performance of the no-arbitrage approach deteriorates in periods of high volatility relative to the equilibrium approach whose performance remains stable and at par with the models with time-varying pricing parameters.

Suggested Citation

  • Jean-Guy Simonato & Lars Stentoft, 2015. "Which pricing approach for options under GARCH with non-normal innovations?," CREATES Research Papers 2015-32, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2015-32
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    File URL: ftp://ftp.econ.au.dk/creates/rp/15/rp15_32.pdf
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    References listed on IDEAS

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    1. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 540-582, Fall.
    2. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    3. Christoffersen, Peter & Heston, Steve & Jacobs, Kris, 2006. "Option valuation with conditional skewness," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 253-284.
    4. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
    5. 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.
    6. Rombouts, Jeroen V.K. & Stentoft, Lars, 2015. "Option pricing with asymmetric heteroskedastic normal mixture models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 635-650.
    7. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
    8. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    9. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    10. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
    11. Lars Stentoft, 2011. "What we can learn from pricing 139,879 Individual Stock Options," CREATES Research Papers 2011-52, Department of Economics and Business Economics, Aarhus University.
    12. 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.
    13. Jin-Chuan Duan & Jean-Guy Simonato, 1998. "Empirical Martingale Simulation for Asset Prices," Management Science, INFORMS, vol. 44(9), pages 1218-1233, September.
    14. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    15. Simonato, Jean-Guy, 2012. "GARCH processes with skewed and leptokurtic innovations: Revisiting the Johnson Su case," Finance Research Letters, Elsevier, vol. 9(4), pages 213-219.
    16. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Badescu, Alexandru & Cui, Zhenyu & Ortega, Juan-Pablo, 2016. "A note on the Wang transform for stochastic volatility pricing models," Finance Research Letters, Elsevier, vol. 19(C), pages 189-196.

    More about this item

    Keywords

    Option pricing; Equilibrium approach; No-arbitrage approach;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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