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Option calibration of exponential Lévy models: Implementation and empirical results

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  • Söhl, Jakob
  • Trabs, Mathias

Abstract

Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models and improve these methods. Confidence intervals are constructed for the estimators in the finite activity case. They allow inference on the behavior of the parameters when the option prices are observed in a sequence of trading days. We compare the performance of the procedures for finite and infinite jump activity based on real option data.

Suggested Citation

  • Söhl, Jakob & Trabs, Mathias, 2012. "Option calibration of exponential Lévy models: Implementation and empirical results," SFB 649 Discussion Papers 2012-017, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2012-017
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    1. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    2. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    3. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    4. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    5. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    6. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    7. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 519-547, July.
    8. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
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    Cited by:

    1. Jakob Sohl, 2012. "Confidence sets in nonparametric calibration of exponential L\'evy models," Papers 1202.6611, arXiv.org, revised Sep 2013.

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    More about this item

    Keywords

    European option; jump diffusion; self-decomposability; confidence sets; nonlinear inverse problem; spectral cut-off;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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