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Option calibration of exponential L\'evy models: Confidence intervals and empirical results

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  • Jakob Sohl
  • Mathias Trabs

Abstract

Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as for self-decomposable L\'evy models. Based on finite sample variances, confidence intervals are constructed for the volatility, for the drift and, pointwise, for the jump density. As demonstrated by simulations, these intervals perform well in terms of size and coverage probabilities. We compare the performance of the procedures for finite and infinite jump activity based on options on the German DAX index and find that both methods achieve good calibration results. The stability of the finite activity model is studied when the option prices are observed in a sequence of trading days.

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  • Jakob Sohl & Mathias Trabs, 2012. "Option calibration of exponential L\'evy models: Confidence intervals and empirical results," Papers 1202.5983, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1202.5983
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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. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    4. 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.
    5. 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.
    6. 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.
    7. 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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