Rate of convergence of binomial formula for option pricing

Abstract

The binomial and Black--Scholes formulas are tools for valuating a call option at any specified time. We have already known that the binomial formula converges to the Black--Scholes formula as the number of periods (n) converges to infinity. In this research, we give the rate of this convergence. Our order is [Equation] which is better than Cox, Ross and Robistein (1979), Leisen and Reimer (1996), Heston and Zhon (2000), Francine and Marc Diener (2004) and Chang and Palmer (2007). We also provide the explicit constant of the bound.