Pricing Double Barrier Options: An Analytical Approach
AbstractDouble 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 InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 97-015/2.
Date of creation: 30 Jan 1997
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double barrier options; option pricing; partial differential equations; Laplace transform; Cauchy's Residue Theorem;
Other versions of this item:
- Antoon Pelsser, . "Pricing Double Barrier Options: An Analytical Approach," Computing in Economics and Finance 1997 130, Society for Computational Economics.
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- Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298.
- 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.
- Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double-Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378.
- 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.
- Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
- Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
- Sbuelz, A., 2000. "Hedging Double Barriers with Singles," Discussion Paper 2000-112, Tilburg University, Center for Economic Research.
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