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Pricing Double Barrier Options: An Analytical Approach

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  • Antoon Pelsser

    (Erasmus University Rotterdam and ING)

Abstract

Double barrier options have become popular instruments in derivative markets. Several papers_new have already analyseddouble knock-out call and put options using different methods. In a recent paper, Geman and Yor (1996) deriveexpressions for the Laplace transform of the double barrrier option price. However, they have to resort to numericalinversion of the Laplace transform to obtain option prices. In this paper, we are able to solve, using contour integration,the inverse of the Laplace transforms analytically thereby eliminating the need for numerical inversion routines. To ourknowledge, this is one of the first applications of contour integration to option pricing problems. To illustrate the power ofthis method, we derive analytical valuation formulas for a much wider variety of double barrier options than has beentreated in the literature so far. Many of these variants are nowadays being traded in the markets. Especially, options whichpay a fixed amount of money (a "rebate") as soon as one of the barriers is hit and double barrier knock-in options.

Suggested Citation

  • Antoon Pelsser, 1997. "Pricing Double Barrier Options: An Analytical Approach," Tinbergen Institute Discussion Papers 97-015/2, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:19970015
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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. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    3. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    4. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double‐Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378, October.
    5. 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.
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    Cited by:

    1. Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
    2. Xiang Wang & Jessica Li & Jichun Li, 2023. "A Deep Learning Based Numerical PDE Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 149-164, June.
    3. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
    4. C. Atkinson & S. Kazantzaki, 2009. "Double knock-out Asian barrier options which widen or contract as they approach maturity," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 329-340.
    5. Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Discussion Paper 2000-112, Tilburg University, Center for Economic Research.
    6. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    7. Pancs Romans, 2010. "Communication, Innovation, and Growth," The B.E. Journal of Macroeconomics, De Gruyter, vol. 10(1), pages 1-54, February.

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