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) less than or equal to P-n-P less than or equal to C/n(3/4). With an additional assumption on the interest rate and the volatility, a better upper bound is derived.