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

Yuan Li, Kenichiro Shiraya, Yuji Umezawa and Akira Yamazaki
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Yuan Li: Graduate School of Economics, University of Tokyo
Kenichiro Shiraya: Graduate School of Economics, University of Tokyo
Akira Yamazaki: Graduate School of Business Administration, Hosei University

No CARF-F-536, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: 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.

Pages: 25
Date: 2022-03
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