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Connecting discrete and continuous path-dependent options

Author

Listed:
  • Paul Glasserman

    (Graduate School of Business, Columbia University, New York, NY 10027, USA)

  • S.G. Kou

    (Department of Statistics, University of Michigan, Ann Arbor, MI 48109-1027, USA)

  • Mark Broadie

    (Graduate School of Business, Columbia University, New York, NY 10027, USA)

Abstract

This paper develops methods for relating the prices of discrete- and continuous-time versions of path-dependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closed-form solutions for continuous option prices to approximate their discrete counterparts. We also develop discrete-time discrete-state lattice methods for determining accurate prices of discrete and continuous path-dependent options. In several cases, the lattice methods use correction terms based on the connection between discrete- and continuous-time prices which dramatically improve convergence to the accurate price.

Suggested Citation

  • Paul Glasserman & S.G. Kou & Mark Broadie, 1999. "Connecting discrete and continuous path-dependent options," Finance and Stochastics, Springer, vol. 3(1), pages 55-82.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:1:p:55-82
    Note: received: December 1996; final version received: December 1997
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    Citations

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    Cited by:

    1. Farid Aitsahlia & Tzeung Le Lai, 1998. "Random walk duality and the valuation of discrete lookback options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 227-240.

    More about this item

    Keywords

    Barrier options; lookback options; continuity corrections; trinomial trees;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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