“Understanding N(d1) and N(d2): Risk-Adjusted Probabilities in the Black-Scholes Model”

By Lars Tyge Nielsen

Finance 14 (1993), 95-106

Abstract

This paper uses risk-adjusted lognormal probabilities to derive the Black- Scholes formula and explain the factors N(d1) and N(d2). It also shows how the one-period and multi-period binomial option pricing formulas can be restated so that they involve analogues of N(d1) and N(d2) which have the same interpretation as in the Black-Scholes model.