On the binomial approximation of the American put

TL;DR

This paper analyzes the accuracy of binomial models in approximating American put option prices within the Black-Scholes framework, establishing an error bound that depends on the number of time steps and market parameters.

Contribution

It provides a new error estimate for the binomial approximation of American put options, highlighting how the approximation error scales with the number of periods and market conditions.

Findings

Error of approximation is O((ln n)^α / n)

Error bound depends on interest rate and dividend yield

Provides theoretical justification for binomial model accuracy

Abstract

We consider the binomial approximation of the American put price in the Black-Scholes model (with continuous dividend yield). Our main result is that the error of approximation is $O((ln n) $\alpha$ /n)$ where n is the number of time periods and the exponent $\alpha$ is a positive number, the value of which may differ according to the respective levels of the interest rate and the dividend yield.