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Primary Article

Pricing Discrete Barrier Options with an Adaptive Mesh Model

Dong-Hyun Ahn, Stephen Figlewski and Bin Gao
The Journal of Derivatives Summer 1999, 6 (4) 33-43; DOI: https://doi.org/10.3905/jod.1999.319127
Dong-Hyun Ahn
An assistant professor of finance at the University of North Carolina in Chapel Hill, North Carolina.
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Stephen Figlewski
A professor of finance at New York University Stern School of Business.
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Bin Gao
An assistant professor of finance at the University of North Carolina in Chapel Hill, North Carolina.
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Abstract

The binomial option pricing model and the trinomial model, its more versatile relative, are invaluable tools for pricing complex derivatives, especially those with American exercise. But while these models converge to the correct option values as the time and price step sizes go to zero, for certain kinds of problems getting close enough may require a very large amount of calculation. The cause is often non-linearity or discontinuity in the option payoff that occurs only in a small region. One example is a barrier option with a barrier that is only monitored at discrete intervals. This article describes how to solve the discrete barrier problem with an adaptive mesh model, a general approach to lattice building that constructs smell sections of fine high-resolution mesh in the critical areas and then grafts them onto a base lattice with coarser time and price steps elsewhere. The technique achieves an increase in accuracy that is quite remarkable.

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The Journal of Derivatives
Vol. 6, Issue 4
Summer 1999
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Pricing Discrete Barrier Options with an Adaptive Mesh Model
Dong-Hyun Ahn, Stephen Figlewski, Bin Gao
The Journal of Derivatives May 1999, 6 (4) 33-43; DOI: 10.3905/jod.1999.319127

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Pricing Discrete Barrier Options with an Adaptive Mesh Model
Dong-Hyun Ahn, Stephen Figlewski, Bin Gao
The Journal of Derivatives May 1999, 6 (4) 33-43; DOI: 10.3905/jod.1999.319127
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