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Pricing Discrete Barrier and Hindsight Options with the Tridiagonal Probability Algorithm

Author

Listed:
  • Wai Man Tse

    (School of Business, The University of Hong Kong, Pokfulam Road, Hong Kong)

  • Leong Kwan Li

    (Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • Kai Wang Ng

    (Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong)

Abstract

This paper develops an algorithm to calculate the Brownian multivariate normal probability subject to any preset error tolerance criteria. The algorithm is founded upon the computational simplicity of the tridiagonal structure of the inverse of the Brownian correlation matrix. Compared with existing pricing technologies without the "barrier too close" problem, our calculation method can produce a more accurate and efficient analytic evaluation of barrier options monitored at discrete instants with well- or ill-behaved barrier levels, or discrete hindsight options, for a reasonably large number of monitorings.

Suggested Citation

  • Wai Man Tse & Leong Kwan Li & Kai Wang Ng, 2001. "Pricing Discrete Barrier and Hindsight Options with the Tridiagonal Probability Algorithm," Management Science, INFORMS, vol. 47(3), pages 383-393, March.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:3:p:383-393
    DOI: 10.1287/mnsc.47.3.383.9775
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    References listed on IDEAS

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    1. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    2. Naoto Kunitomo & Masayuki Ikeda, 1992. "Pricing Options With Curved Boundaries1," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 275-298, October.
    3. Mark Schroder, 1989. "A Reduction Method Applicable to Compound Option Formulas," Management Science, INFORMS, vol. 35(7), pages 823-827, July.
    4. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349, October.
    5. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    6. Phelim Boyle & Yisong Tian, 1998. "An explicit finite difference approach to the pricing of barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 17-43.
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    Cited by:

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    3. M. Broadie & Y. Yamamoto, 2005. "A Double-Exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-Dependent Options," Operations Research, INFORMS, vol. 53(5), pages 764-779, October.

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