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

Abstract

We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) 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.

Minor typos corrected + DOI added + MSC classes added

References in corpus (2)

• On expansions for the Black-Scholes prices and hedge parameters
• Determination of the Lévy Exponent in Asset Pricing Models