Comparing the Convergence Behaviour of Binomial and Trinomial Models

An American option differs from a European one by the early exercise possibility. An American option can be exercised at any time up to the maturity date. In general, there is unfortunately no analytical solution to the American option problem. Binomial and trinomial approximations are useful to solve this problem but using a lattice model introduces approximation error. Both models have the property of convergence to Black & Scholes prices thus; can be used alternatively to solve the Black & Scholes partial differential equation. This paper presents the suitable conditions under which the two models converge to Black & Scholes and compares the convergence behaviour in order to question their efficiency.