Down-and-out European call
= Down-and-out European call
{title2=$(S_T-K)_+\mathbf1_{\{\min_{0\le t\le T}S_t>B\}}$}
A <down-and-out European call> pays the usual <European call option> payoff only if a lower barrier has not been hit before maturity. In the zero-interest, zero-dividend <Black-Scholes model>, for $0<B\le K<S$, its value is $C(S,K)-(S/B)C(B^2/S,K)$. This follows from reflection of the drifted logarithmic price killed at the barrier.