Working Papers

Quantitative Finance




Moments of Maximum of Lévy Processes: Application to Barrier and Lookback Option Pricing

Author:Yuan Li, Kenichiro Shiraya, Yuji Umezawa, Akira Yamazaki


We propose an analytical method to calculate mixed moments between the terminal value and the maximum of a Lévy process. The method derives the moments directly from the Wiener-Hopf factors without finding density or characteristic functions. The advantage of this method is that it is computationally fast and stable. Furthermore, it can be applied to a wide class of Lévy processes. Numerical experiments show that our method provides sufficiently accurate values of the moments. We then apply it to a Monte Carlo simulation for the pricing of barrier and lookback options. The results show that our simulation method can greatly reduce the time discretization error.