In the Black-Scholes framework, d2 is defined in relation to d1. Which expression correctly defines d2?

• A. d2 = d1 - σ√(T-t)
• B. d2 = d1 + σ√(T-t)
• C. d2 = ln(S_t/K)/(σ√(T-t)) + (r - σ^2/2)√(T-t)
• D. d2 = (ln(S_t/K) + (r + σ^2/2)(T-t))/(σ√(T-t))

Answer: (A)

In Black-Scholes, d1 and d2 are two standardized variables used in the option pricing formulas, and d2 is obtained by subtracting σ times the square root of the time to expiration from d1. With τ = T − t, d1 = [ln(S_t/K) + (r + 0.5 σ^2) τ] / (σ√τ). Subtracting σ√τ gives d2 = d1 − σ√τ, which also equals [ln(S_t/K) + (r − 0.5 σ^2) τ] / (σ√τ). So the correct definition is d2 = d1 − σ√(T−t).

The other forms either place the terms in the wrong places or produce what is effectively the d1 expression rather than d2, or mix in √τ where τ should be used, causing dimensional inconsistency. This is why the simple subtraction relation accurately captures the link between d1 and d2 used in the Black-Scholes formulas.