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 \(\mathbb {C}\) or \(\mathbb {C}^2\). Comparisons with numerical methods and efficiency tests are also discussed.
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Aguilar, JP. The value of power-related options under spectrally negative Lévy processes. Rev Deriv Res 24, 173–196 (2021). https://doi.org/10.1007/s11147-020-09174-0
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DOI: https://doi.org/10.1007/s11147-020-09174-0
Keywords
- Lévy process
- Stable distribution
- Tempered stable distribution
- Digital option
- Power option
- Gap option
- Log option