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The Valuation of American Barrier Options Using the Decomposition Technique

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  • B. Gao J. Huang
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    Abstract

    In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call "symmetry" relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options.

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    File URL: http://www.stern.nyu.edu/fin/workpapers/papers99/wpa99002.pdf
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    Bibliographic Info

    Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 99-002.

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    Handle: RePEc:fth:nystfi:99-002

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    Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
    Phone: (212) 998-0100
    Web page: http://w4.stern.nyu.edu/finance/
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    1. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-91.
    2. Mark Schroder, 1989. "A Reduction Method Applicable to Compound Option Formulas," Management Science, INFORMS, vol. 35(7), pages 823-827, July.
    3. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
    4. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June.
    5. Kim, In Joon, 1990. "The Analytic Valuation of American Options," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-72.
    6. Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. " The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-40, June.
    7. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
    8. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    9. Peter Carr & Robert Jarrow & Ravi Myneni, 1992. "Alternative Characterizations Of American Put Options," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 87-106.
    10. L.C.G. Rogers & E.J. Stapleton, 1997. "Fast accurate binomial pricing," Finance and Stochastics, Springer, vol. 2(1), pages 3-17.
    11. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    12. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
    13. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    14. 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.
    15. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    16. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
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