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Quantile estimation for Lévy measures

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  • Trabs, Mathias

Abstract

Generalizing the concept of quantiles to the jump measure of a Lévy process, the generalized quantiles qτ±>0, for τ>0, are given by the smallest values such that a jump larger than qτ+ or a negative jump smaller than −qτ−, respectively, is expected only once in 1/τ time units. Nonparametric estimators of the generalized quantiles are constructed using either discrete observations of the process or using option prices in an exponential Lévy model of asset prices. In both models minimax convergence rates are shown. Applying Lepski’s approach, we derive adaptive quantile estimators. The performance of the estimation method is illustrated in simulations and with real data.

Suggested Citation

  • Trabs, Mathias, 2015. "Quantile estimation for Lévy measures," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3484-3521.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:9:p:3484-3521
    DOI: 10.1016/j.spa.2015.04.004
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    References listed on IDEAS

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    Cited by:

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    3. Todorov, Viktor, 2022. "Nonparametric jump variation measures from options," Journal of Econometrics, Elsevier, vol. 230(2), pages 255-280.

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