European Option Pricing with the Binomial Tree: Convergence to Black Scholes

This paper explores the Binomial pricing model as applied to European options. Originally developed as a teaching tool, the model has since become a powerful framework for pricing more complex derivatives, including American options.

The study outlines the mathematical foundations of the Binomial approach, explains its algorithmic implementation, and demonstrates how the model’s discrete step method converges to the continuous Black–Scholes formula. This highlights the deep connection between discrete-time and continuous-time option valuation methods.