Black–Scholes option pricing model — Accounting glossary

For a European call on a non-dividend-paying underlying, C = S×N(d1) − K×e^(−rT)×N(d2), where d1 = [ln(S/K) + (r + σ²/2)T]/(σ√T) and d2 = d1 − σ√T. Inputs must use compatible time units and volatility conventions. Assumptions include idealised trading, constant volatility and rates and the specified payoff/exercise structure. Real-option applications use project analogues of these inputs, but non-traded assets, changing risk and managerial constraints limit precision. A model value is conditional on the inputs rather than a guaranteed transaction price.

Worked example

For an illustrative non-dividend-paying underlying with S=100, K=100, r=0, T=1 and volatility 20%, d1=0.1 and d2=−0.1. With N(0.1)=0.539828 and N(−0.1)=0.460172, call value is about 7.9656.

Common mistake

Using 20 rather than 0.20 for 20% volatility, mixing months and years, or treating a project valuation input as directly observable when it is estimated.

Where it appears in your exams

Qualification	Exam	Relationship	Period
ACCA	AFM	Direct	September 2026–June 2027