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Approximation Method Using Black-Scholes Formula for Barrier Option Pricing under Lévy Models

Author

Listed:
  • Yuan Li

    (Graduate School of Economics, University of Tokyo)

  • Kaimon Miyachi

    (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)

Abstract

This study proposes an approximation method for pricing continuously monitored barrier options. We employ a class of Lévy processes as the driving factor of an underlying stock price and consider a mimicking process for approximation. Randomizing the Black-Scholes formula associated with the mimicking process leads to a primary approximation formula. We then develop a probability matching adjustment for improving the accuracy of the primary approximation formula. This method is straightforward and easily implementable. Nevertheless, the approximation prices are reasonably accurate, and the calculation speed is remarkably fast, regardless of time to maturity.

Suggested Citation

  • Yuan Li & Kaimon Miyachi & Kenichiro Shiraya & Akira Yamazaki, 2019. "Approximation Method Using Black-Scholes Formula for Barrier Option Pricing under Lévy Models," CARF F-Series CARF-F-454, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jun 2021.
    • Handle: RePEc:cfi:fseres:cf454
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    References listed on IDEAS

    as
    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    2. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Shiraya, Kenichiro & Uenishi, Hiroki & Yamazaki, Akira, 2020. "A general control variate method for Lévy models in finance," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1190-1200.

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