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Confidence sets in nonparametric calibration of exponential L\'evy models

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  • Jakob Sohl

Abstract

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential L\'evy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration method for the estimators of the volatility, the drift, the jump intensity and the L\'evy density at finitely many points.

Suggested Citation

  • Jakob Sohl, 2012. "Confidence sets in nonparametric calibration of exponential L\'evy models," Papers 1202.6611, arXiv.org, revised Sep 2013.
    • Handle: RePEc:arx:papers:1202.6611
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    References listed on IDEAS

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    1. 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.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    4. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, vol. 10(4), pages 449-474, December.
    5. Belomestny, Denis, 2009. "Spectral estimation of the fractional order of a Lévy process," SFB 649 Discussion Papers 2009-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    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. 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.
    8. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print halshs-00002695, HAL.
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