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

Author

Listed:
  • Yuan Li

    (Graduate School of Economics, University of Tokyo)

  • Kenichiro Shiraya

    (Graduate School of Economics, University of Tokyo)

  • Yuji Umezawa
  • Akira Yamazaki

    (Graduate School of Business Administration, Hosei University)

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.

Suggested Citation

  • Yuan Li & Kenichiro Shiraya & Yuji Umezawa & Akira Yamazaki, 2022. "Moments of Maximum of Lévy Processes: Application to Barrier and Lookback Option Pricing," CARF F-Series CARF-F-536, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf536
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    References listed on IDEAS

    as
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    5. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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