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American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison

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  • Lars Stentoft

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

Abstract

This paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We first of all show that with a particular choice of framework the parameters of the SV models can be estimated using simple maximum likelihood techniques. Hence the two types of models can be implemented in an internally consistent manner. We then perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. The results show that there are differences between the two models, though the discrete time GARCH prices converge quickly to the continuous time SV values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results show that, while the overall differences in performance are small, for the in the money put options on individual stocks the continuous time SV models do generally perform better than the discrete time GARCH specifications.

Suggested Citation

  • Lars Stentoft, 2011. "American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison," CREATES Research Papers 2011-34, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-34
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    References listed on IDEAS

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    Cited by:

    1. Hafner, Christian M. & Laurent, Sebastien & Violante, Francesco, 2017. "Weak Diffusion Limits Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(03), pages 691-716, June.
    2. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147 Edward Elgar Publishing.
    3. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.

    More about this item

    Keywords

    American Options; Augmented GARCH; Least Squares Monte Carlo; Stochastic Volatility;

    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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