Down-and-out digital call
= Down-and-out digital call
A <digital call option> that pays its terminal indicator only if a lower barrier was avoided. When its strike equals the lower barrier, survival already implies the terminal indicator is one. It is then a <no-touch option>, with alive price $C_d(s,t;B)-(s/B)^{1-2r/\sigma^2}C_d(B^2/s,t;B)$ in the dividend-free <Black-Scholes model>.