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A Discrete Time Approach for European and American Barrier Options

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  • K. Sandmann
  • Reimer, M.

Abstract

The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider analytically and numerically the convergence of the prices in discrete time to their continuous-time limits. The arising numerical problems are solved by quadratic interpolation. Furthermore, the case of American barrier options is analyzed in detail. For American barrier call options, binomial formulae and their limit results are given. Finally, the binomial approach is applied to contracts with local and partial barrier checks.(Completely revised version march 1995)

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 272.

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Date of creation: Mar 1995
Date of revision:
Handle: RePEc:bon:bonsfb:272

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

Keywords: Arbitrage; Barrier Option; Option Pricing; Path dependent payoff;

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References

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  1. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
  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, American Finance Association, vol. 34(5), pages 1111-27, December.
  3. Reimer, Matthias & Klaus Sandmann, 1993. "Down-and-out Call - Bewertungstheorie, numerische Verfahren und Simulationsstudie," Discussion Paper Serie B, University of Bonn, Germany 239, University of Bonn, Germany.
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  6. Rendleman, Richard J, Jr & Bartter, Brit J, 1979. "Two-State Option Pricing," Journal of Finance, American Finance Association, American Finance Association, vol. 34(5), pages 1093-1110, December.
  7. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
  8. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, American Finance Association, vol. 31(2), pages 351-67, May.
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Citations

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Cited by:
  1. Tatjana Chudjakow & Jörg Vorbrink, 2009. "Exercise Strategies for American Exotic Options under Ambiguity," Working Papers 421, Bielefeld University, Center for Mathematical Economics.
  2. Jin-Chuan Duan & Evan Dudley & Geneviève Gauthier & Jean-Guy Simonato, 1999. "Pricing Discretely Monitored Barrier Options by a Markov Chain," CIRANO Working Papers, CIRANO 99s-15, CIRANO.
  3. Elisa Appolloni & Andrea Ligori, 2014. "Efficient tree methods for pricing digital barrier options," Papers 1401.2900, arXiv.org, revised Jan 2014.
  4. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 24(11-12), pages 1563-1590, October.

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