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Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals

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  • Kensuke Ishitani

Abstract

This paper presents a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.

Suggested Citation

  • Kensuke Ishitani, 2016. "Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals," Papers 1611.05194, arXiv.org, revised Dec 2016.
    • Handle: RePEc:arx:papers:1611.05194
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Takashi Kato & Akihiko Takahashi & Toshihiro Yamada, 2014. "A Semi-group Expansion for Pricing Barrier Options," CARF F-Series CARF-F-349, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Yoshifumi Muroi, 2006. "Pricing Lookback Options with Knock-out Boundaries," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 155-190.
    4. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    5. Shigeto Kusuoka & Mariko Ninomiya & Syoiti Ninomiya, 2012. "Application Of The Kusuoka Approximation To Barrier Options," CARF F-Series CARF-F-277, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
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