black76F <- function(type=c("call","put"),F, X, T, Tf, r, sigma) {
d1 <- ( log(F/X) + (sigma^2/2)*T ) / (sigma*sqrt(T))
d2 <- d1 - sigma*sqrt(T)
if(match.arg(type)=="call")
exp(-r*Tf) * (F*pnorm(d1) - X*pnorm(d2))
}
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