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Fast accurate binomial pricing

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  • 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.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 2 (1997)
Issue (Month): 1 ()
Pages: 3-17

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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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Related research

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

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Citations

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Cited by:
  1. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
  2. Yan Dolinsky & Yuri Kifer, 2009. "Binomial Approximations for Barrier Options of Israeli Style," Papers 0907.4136, arXiv.org.
  3. Marti G. Subrahmanyam & Bin Gao & Jing-zhi Huang, 1998. "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-067, New York University, Leonard N. Stern School of Business-.
  4. Emmanuel Gobet, 2009. "Advanced Monte Carlo methods for barrier and related exotic options," Post-Print hal-00319947, HAL.
  5. B. Gao J. Huang, . "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-.
  6. Leisen, Dietmar, 1997. "The Random-Time Binomial Model," Discussion Paper Serie B 399, University of Bonn, Germany.

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