On the rate of convergence of discrete-time contingent claims

This paper characterizes the rate of convergence of discrete-time multinomi al option prices. We show that the rate of convergence depends on the smoot hness of option payoff functions, and is much lower than commonly believed because option payoff functions are often of all-or-nothing type and are no t continuously differentiable. To improve the accuracy, we propose two simp le methods, an adjustment of the discrete-time solution prior to maturity a nd smoothing of the payoff function, which yield solutions that converge to their continuous-time limit at the maximum possible rate enjoyed by smooth payoff functions. We also propose an intuitive approach that systematicall y derives multinomial models by matching the moments of a normal distributi on. A highly accurate trinomial model also is provided for interest rate de rivatives. Numerical examples are carried out to show that the proposed met hods yield fast and accurate results.