Connecting discrete and continuous lookback or hindsight options in exponential L\'evy models

TL;DR

This paper investigates the differences between continuous and discrete supremum values of Lévy processes, extending existing results to jump-diffusion models and providing bounds for general exponential Lévy models, with implications for lookback option pricing.

Contribution

It extends prior work on supremum differences to include jump-diffusion models and derives bounds for general exponential Lévy models, enhancing option pricing methods.

Findings

Extended supremum difference results to jump-diffusion models

Derived bounds for exponential Lévy models

Implications for lookback option pricing

Abstract

Motivated by the pricing of lookback options in exponential L\'evy models, we study the difference between the continuous and discrete supremum of L\'evy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential L\'evy models.