Teaching the Economics and Convergence of the Binomial and the Black-Scholes Option Pricing Formulas

Authors

Abstract

This paper simplifies the economics of option pricing formulas by clarifying how the no-arbitrage principle ensures that a risk-neutral valuation relationship (based on risk-neutral probabilities) exists between an option and its underlying asset. A spreadsheet exercise shows how binomial probabilities and prices numerically converge to Black-Scholes probabilities and prices, and further numerical analysis reveals how the histogram of terminal stock returns in the multi-period binomial tree converges in probability to the normal distribution. Recommendations for teaching option pricing and convergence include the use of a hypothetical case study of a graduating student’s comparison of competing salary offers.

Recommended Citation

(2026) "Teaching the Economics and Convergence of the Binomial and the Black-Scholes Option Pricing Formulas," Journal of Economics and Finance Education: Vol. 19: Iss. 1, Article 4.
Available at: https://scholarship.rollins.edu/jefe/vol19/iss1/4