Journal of Risk

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The convergence of binomial trees for pricing the American put

Mark S. Joshi

ABSTRACT

We study 20 different implementation methodologies for each of 11 different choices of parameters of binomial trees and investigate the speed of convergence for pricing American put options numerically. We conclude that the most effective methods involve using truncation, Richardson extrapolation and sometimes smoothing.We do not recommend the use of a European as a control. The most effective trees are the Tian third-order moment matching tree and a new tree designed to minimize oscillations.

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