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Discrete time option pricing with flexible volatility estimation

Author

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  • Christian M. Hafner

    (CORE, UniversitÊ catholique de Louvain, Louvain-la-Neuve, Belgium)

  • Wolfgang HÄrdle

    (Institut fØr Statistik und ãkonometrie, Humboldt-UniversitÄt zu Berlin, Spandauer Str. 1, D-10178 Berlin, Germany)

Abstract

By extending the GARCH option pricing model of Duan (1995) to more flexible volatility estimation it is shown that the prices of out-of-the-money options strongly depend on volatility features such as asymmetry. Results are provided for the properties of the stationary pricing distribution in the case of a threshold GARCH model. For a stock index series with a pronounced leverage effect, simulated threshold GARCH option prices are substantially closer to observed market prices than the Black/Scholes and simulated GARCH prices.

Suggested Citation

  • Christian M. Hafner & Wolfgang HÄrdle, 2000. "Discrete time option pricing with flexible volatility estimation," Finance and Stochastics, Springer, vol. 4(2), pages 189-207.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:189-207
    Note: received: August 1997; final version received: April 1999
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    Cited by:

    1. Anna Pajor, 2009. "Bayesian Analysis of the Box-Cox Transformation in Stochastic Volatility Models," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 9, pages 81-90.
    2. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, Department of Economics and Business Economics, Aarhus University.
    3. Ignacio Mauleon & Javier Perote, 2000. "Testing densities with financial data: an empirical comparison of the Edgeworth-Sargan density to the Student's t," The European Journal of Finance, Taylor & Francis Journals, vol. 6(2), pages 225-239.
    4. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    5. Badescu, Alexandru M. & Kulperger, Reg J., 2008. "GARCH option pricing: A semiparametric approach," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 69-84, August.
    6. Hafner, Christian M. & Herwartz, Helmut, 2001. "Option pricing under linear autoregressive dynamics, heteroskedasticity, and conditional leptokurtosis," Journal of Empirical Finance, Elsevier, vol. 8(1), pages 1-34, March.
    7. Matthias R. Fengler & Alexander Melnikov, 2018. "GARCH option pricing models with Meixner innovations," Review of Derivatives Research, Springer, vol. 21(3), pages 277-305, October.
    8. Mozumder, Sharif & Frijns, Bart & Talukdar, Bakhtear & Kabir, M. Humayun, 2024. "On practitioners closed-form GARCH option pricing," International Review of Financial Analysis, Elsevier, vol. 94(C).
    9. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
    10. Jacobi, Frank, 2005. "ARCH-Prozesse und ihre Erweiterungen - Eine empirische Untersuchung für Finanzmarktzeitreihen -," Arbeitspapiere des Instituts für Statistik und Ökonometrie 31, Johannes Gutenberg-Universität Mainz, Institut für Statistik und Ökonometrie.
    11. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Pricing individual stock options using both stock and market index information," Journal of Banking & Finance, Elsevier, vol. 111(C).
    12. 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.
    13. Härdle, Wolfgang & Sperlich, Stefan, 1997. "Financial calculations on the net," SFB 373 Discussion Papers 1997,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Jin-Chuan Duan & Peter H. Ritchken & Zhiqiang Sun, 2006. "Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities," Working Papers (Old Series) 0619, Federal Reserve Bank of Cleveland.
    15. Babsiri, Mohamed El & Zakoian, Jean-Michel, 2001. "Contemporaneous asymmetry in GARCH processes," Journal of Econometrics, Elsevier, vol. 101(2), pages 257-294, April.
    16. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers 2002s-33, CIRANO.
    17. Peter Christoffersen & Kris Jacobs, 2004. "Which GARCH Model for Option Valuation?," Management Science, INFORMS, vol. 50(9), pages 1204-1221, September.
    18. Thorsten Lehnert & Gildas Blanchard & Dennis Bams, 2014. "Evaluating Option Pricing Model Performance Using Model Uncertainty," LSF Research Working Paper Series 14-06, Luxembourg School of Finance, University of Luxembourg.
    19. Duan, Jin-Chuan & Wei, Jason, 2005. "Executive stock options and incentive effects due to systematic risk," Journal of Banking & Finance, Elsevier, vol. 29(5), pages 1185-1211, May.
    20. Papantonis, Ioannis, 2016. "Volatility risk premium implications of GARCH option pricing models," Economic Modelling, Elsevier, vol. 58(C), pages 104-115.
    21. Radovan Parrák, 2013. "The Economic Valuation of Variance Forecasts: An Artificial Option Market Approach," Working Papers IES 2013/09, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Aug 2013.

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    More about this item

    Keywords

    Option pricing; volatility; GARCH; threshold GARCH; leverage effect;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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