Convergence of American Option Values From Discrete‐ to Continuous‐time Financial Models¹

Given a sequence of discrete‐time option valuation models in which the sequence of processes defining the state variables converges weakly to a diffusion, we prove that the sequence of American option values obtained from these discrete‐time models also converges to the corresponding value obtained from the continuous‐time model for the standard models in the finance/economics literature. the convergence proof carries over to the case when the limiting risky asset price process follows a diffusion, except it pays discrete dividends on some fixed dates.