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Confidence sets in nonparametric calibration of exponential Lévy models

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  • Jakob Söhl
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    Abstract

    Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy density at nitely many points in the spectral calibration method. Furthermore, the asymptotic normality result leads to a test on the value of the volatility in exponential Lévy models.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2012-012.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2012-012.

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    Length: 46 pages
    Date of creation: Feb 2012
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2012-012

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    Related research

    Keywords: European option; Jump diffusion; Confidence sets; Asymptotic normality; Nonlinear inverse problem;

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    1. Denis Belomestny, 2009. "Spectral estimation of the fractional order of a Lévy process," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2009-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Rama Cont, 2006. "Model uncertainty and its impact on the pricing of derivative instruments," Post-Print, HAL halshs-00002695, HAL.
    3. Denis Belomestny & Markus Reiß, 2006. "Spectral calibration of exponential Lévy models," Finance and Stochastics, Springer, Springer, vol. 10(4), pages 449-474, December.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 125-144.
    5. Rama Cont, 2006. "Model Uncertainty And Its Impact On The Pricing Of Derivative Instruments," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 16(3), pages 519-547.
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