Error estimates for the binomial approximation of American put options

Abstract

We establish some error estimates for the binomial approximation of American put prices in the Black-Scholes model. Namely, we prove that if P is the American put price and $P_n$ its n-step binomial approximation, there exist positive constants c and C such that $-c/n^{2/3} \leq P_n - P \leq C/n^{3/4}$. With an additional assumption on the interest rate and the volatility, a better upper bound is derived.