Closed-form European call price under GBM with constant r, σ: C = S_0,N(d_1) - K,e^-rT,N(d_2), where d_1 = dfracln(S_0/K) + (r + tfrac12σ^2)Tσ√(T) and d_2 = d_1 - σ√(T). Put follows from put-call parity. N(d_2) is the risk-neutral probability of finishing in-the-money; N(d_1) is the delta. The formula is a benchmark, not a belief — it is used to quote and risk-manage in implied-vol space, where its flat-vol assumption is visibly violated by the skew/surface.