A comparison of lattice based option pricing models on the rate of convergence

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 true prices thus, can be used alternatively to solve the Black & Scholes partial differential equation. This paper compares the rate of convergence of the lattice based option pricing models. The comparison is based on the number of nodes produced, computer time used and the approximation error. An illustrative example is used to compare the convergence speed of these two models. Comparing the lattice based option pricing models with respect to different stock prices is taken into consideration.