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. This research obtains the rate of this convergence, namely $\frac{1}{n\sqrt{n}}.$ Our rate of convergence is better than those obtained by Cox, Ross, and Rubinstein (1979), Leisen and Reimer (1996), Heston and Zhon (2000), Diener and Diener (2004) and Chang and Palmer (2007). We also provide the explicit constant of the bound of this convergence.

Keywords:

• Binomial model
• black–schole model
• option pricing

Math classification:

• 62P05

Acknowledgments

The authors would like to thank the referees for all valuable comments and suggestions.