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Fast accurate binomial pricing

Author

Listed:
  • L.C.G. Rogers

    () (University of Bath, School of Mathematical Sciences, Bath BA2 7AY, Great Britain)

  • E.J. Stapleton

    () (University of Bath, School of Mathematical Sciences, Bath BA2 7AY, Great Britain)

Abstract

We discuss here an alternative interpretation of the familiar binomial lattice approach to option pricing, illustrating it with reference to pricing of barrier options, one- and two-sided, with fixed, moving or partial barriers, and also the pricing of American put options. It has often been observed that if one tries to price a barrier option using a binomial lattice, then one can find slow convergence to the true price unless care is taken over the placing of the grid points in the lattice; see, for example, the work of Boyle & Lau [2]. The placing of grid points is critical whether one uses a dynamic programming approach, or a Monte Carlo approach, and this can make it difficult to compute hedge ratios, for example. The problems arise from translating a crossing of the barrier for the continuous diffusion process into an event for the binomial approximation. In this article, we show that it is not necessary to make clever choices of the grid positioning, and by interpreting the nature of the binomial approximation appropriately, we are able to derive very quick and accurate pricings of barrier options. The interpretation we give here is applicable much more widely, and helps to smooth out the `odd-even' ripples in the option price as a function of time-to-go which are a common feature of binomial lattice pricing.

Suggested Citation

  • L.C.G. Rogers & E.J. Stapleton, 1997. "Fast accurate binomial pricing," Finance and Stochastics, Springer, vol. 2(1), pages 3-17.
  • Handle: RePEc:spr:finsto:v:2:y:1997:i:1:p:3-17
    Note: received: November 1996; final version received: April 1997
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    Citations

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    Cited by:

    1. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    2. Yan Dolinsky & Yuri Kifer, 2009. "Binomial Approximations for Barrier Options of Israeli Style," Papers 0907.4136, arXiv.org.
    3. Leisen, Dietmar, 1997. "The Random-Time Binomial Model," Discussion Paper Serie B 399, University of Bonn, Germany.
    4. Emmanuel Gobet, 2009. "Advanced Monte Carlo methods for barrier and related exotic options," Post-Print hal-00319947, HAL.
    5. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 330-344.
    6. Gao, Bin & Huang, Jing-zhi & Subrahmanyam, Marti, 2000. "The valuation of American barrier options using the decomposition technique," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1783-1827, October.
    7. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.

    More about this item

    Keywords

    Binomial pricing; barrier option; American option; Brownian motion;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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