Error estimates for the binomial approximation of American put options

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 Pn its n-step binomial approximation, there exist positive constants c and C such that .c/n2/3.Pn.P.C/n3/4. With an additional assumption on the interest rate and the volatility, a better upper bound is derived.