QuoteEven simpler, PWOQF p109 shows that a binary/digital call has value e^{-rT}N(d2)It is better to use the aproximation that Val wrote: Digital_Call(S,K,r,T)=Cash_Amount*[Call(S,K-0.5*epsi, vol1)-Call(S,K+0.5*epsi, vol2)]/epsi. If not, you are not taking into account the smile.