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Valuation of Barrier Options in a Black--Scholes Setup with Jump Risk

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  • Dietmar P.J. Leisen
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    Abstract

    This paper discusses the pitfalls in the pricing of barrier options a pproximations of the underlying continuous processes via discrete lattice models. These problems are studied first in a Black-Scholes model. Improvements result from a trinomial model and a further modified model where price changes occur at the jump times of a Poisson process. After the numerical difficulties have been resolved in the Black-Scholes model, unpredictable discontinuous price movements are incorporated.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb446.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 446.

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    Length: pages
    Date of creation: Jan 1999
    Date of revision:
    Handle: RePEc:bon:bonsfb:446

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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: binomial model; option valuation; lattice--approach; barrier option;

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    References

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    1. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298.
    4. 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.
    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. Victor Vaugirard, 2001. "Monte Carlo applied to exotic digital options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(3), pages 183-196.

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