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# EuropeanCallBE.R -- version 2010-12-28
EuropeanCallBE <- function(S0, X, r, T, sigma, M) {
# compute constants
dt <- T/M
u <- exp(sigma * sqrt(dt))
d <- 1/u
p <- (exp(r * dt) - d)/(u - d)
# initialize asset prices at maturity (period M)
C <- pmax(S0 * d^(M:0) * u^(0:M) - X, 0)
# log/cumsum version
csl <- cumsum(log(c(1,1:M)))
tmp <- csl[M+1] - csl - csl[(M+1):1] +
log(p) * (0:M) + log(1-p) * (M:0)
C0 <- exp(-r * T) * sum(exp(tmp) * C)
C0
}
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