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Lévy density estimation via information projection onto wavelet subspaces

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  • Song, Seongjoo

Abstract

This paper proposes a nonparametric method for producing smooth and positive estimates of the density of a Lévy process, which is widely used in mathematical finance. We use the method of logwavelet density estimation to estimate the Lévy density with discretely sampled observations. Since Lévy densities are not necessarily probability densities, we introduce a divergence measure similar to Kullback-Leibler information to measure the difference between two Lévy densities. Rates of convergence are established over Besov spaces.

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  • Song, Seongjoo, 2010. "Lévy density estimation via information projection onto wavelet subspaces," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1623-1632, November.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:21-22:p:1623-1632
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    References listed on IDEAS

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    1. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    2. Belomestny, Denis & Reiß, Markus, 2006. "Spectral calibration of exponential Lévy Models [1]," SFB 649 Discussion Papers 2006-034, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    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. Koo, Ja-Yong & Kim, Woo-Chul, 1996. "Wavelet density estimation by approximation of log-densities," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 271-278, February.
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    Cited by:

    1. Akakpo, Nathalie, 2017. "Multivariate intensity estimation via hyperbolic wavelet selection," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 32-57.

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