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Pricing Double Barrier Options: An Analytical Approach

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  • Antoon Pelsser

    (Erasmus University Rotterdam)

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.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 1997 with number 130.

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Handle: RePEc:sce:scecf7:130

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Postal: CEF97, Stanford University, Department of Economics, Stanford CA USA
Web page: http://bucky.stanford.edu/cef97/
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  1. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  2. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double-Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378.
  3. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298.
  4. 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 1111-27, December.
  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 637-54, 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. Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Discussion Paper 2000-112, Tilburg University, Center for Economic Research.
  3. Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.

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