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Efficient static replication of European options under exponential Lévy models

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  • Akihiko Takahashi
  • Akira Yamazaki

Abstract

This study proposes a new scheme for the static replication of European options and their portfolios. First, a general approximation formula for efficient static replication as an extension of Carr P. and Chou A. (1997, 2002) and Carr P. and Wu L. (2002) is derived. Second, a concrete procedure for implementing the scheme by applying it to plain vanilla options under exponential Lévy models is presented. Finally, numerical examples in a model developed by Carr, P., Geman, H., Madan, D., and Yor M. (2002) are used to demonstrate that the replication scheme is more efficient and more effective in practice than a standard static replication method. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 29:1–15, 2009

Suggested Citation

  • Akihiko Takahashi & Akira Yamazaki, 2009. "Efficient static replication of European options under exponential Lévy models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 29(1), pages 1-15, January.
    • Handle: RePEc:wly:jfutmk:v:29:y:2009:i:1:p:1-15
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    Cited by:

    1. Jingtang Ma & Dongya Deng & Harry Zheng, 2016. "Convergence analysis and optimal strike choice for static hedges of general path-independent pay-offs," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 593-603, April.
    2. C. E. Phelan & D. Marazzina & G. Germano, 2020. "Pricing methods for α-quantile and perpetual early exercise options based on Spitzer identities," Quantitative Finance, Taylor & Francis Journals, vol. 20(6), pages 899-918, June.
    3. Balbás, Alejandro & Serna, Gregorio, 2024. "Selling options to beat the market: Further empirical evidence," Research in International Business and Finance, Elsevier, vol. 67(PB).
    4. Adam W. Kolkiewicz, 2016. "Efficient Hedging Of Path–Dependent Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-27, August.
    5. Akira Yamazaki, 2022. "Recovering subjective probability distributions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1234-1263, July.
    6. Ludovic Mathys, 2019. "Valuing Tradeability in Exponential L\'evy Models," Papers 1912.00469, arXiv.org, revised Feb 2020.

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