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

Jean-Philippe Aguilar ()
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Jean-Philippe Aguilar: Covéa Finance - Quantitative Research Team

Review of Derivatives Research, 2021, vol. 24, issue 2, No 4, 173-196

Abstract: 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.

Keywords: Lévy process; Stable distribution; Tempered stable distribution; Digital option; Power option; Gap option; Log option; 60E07; 60G51; 60G52; 62P05; 91G20 (search for similar items in EconPapers)
JEL-codes: C02 C63 G13 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11147-020-09174-0

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