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The value of power-related options under spectrally negative Lévy processes

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  • Jean-Philippe Aguilar

    (Covéa Finance - Quantitative Research Team)

Abstract

We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options etc.) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of the time-to-maturity; these series are obtained via a factorized integral representation in the Mellin space evaluated by means of residues in $$\mathbb {C}$$ C or $$\mathbb {C}^2$$ C 2 . Comparisons with numerical methods and efficiency tests are also discussed.

Suggested Citation

  • Jean-Philippe Aguilar, 2021. "The value of power-related options under spectrally negative Lévy processes," Review of Derivatives Research, Springer, vol. 24(2), pages 173-196, July.
    • Handle: RePEc:kap:revdev:v:24:y:2021:i:2:d:10.1007_s11147-020-09174-0
    DOI: 10.1007/s11147-020-09174-0
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    References listed on IDEAS

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    More about this item

    Keywords

    Lévy process; Stable distribution; Tempered stable distribution; Digital option; Power option; Gap option; Log option;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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