The value of power-related options under spectrally negative L\'evy processes

TL;DR

This paper develops analytical pricing formulas for exotic power options within exponential Lévy models driven by spectrally negative processes, using Mellin space techniques for efficient computation.

Contribution

It introduces new series-based pricing formulas for exotic power options under spectrally negative Lévy processes, enhancing computational efficiency and accuracy.

Findings

Formulas are fast converging series in log-moneyness and time-to-maturity.

Comparison with numerical methods shows high accuracy and efficiency.

Applicable to models driven by stable or tempered stable processes.

Abstract

We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy 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.