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# EuropeanCall.R -- version 2010-12-28
EuropeanCall <- function(S0,X,r,T,sigma,M) {
# compute constants
f7 <- 1; dt <- T/M; v <- exp(-r * dt)
u <- exp(sigma * sqrt(dt)); d <- 1/u
p <- (exp(r * dt) - d) / (u - d)
# initialize asset prices at maturity (period M)
S <- numeric(M + 1)
S[f7+0] <- S0 * d^M
for (j in 1:M) S[f7+j] <- S[f7+j - 1] * u / d
# initialise option values at maturity (period M)
C <- pmax(S - X, 0)
# step back through the tree
for (i in seq(M-1, 0, by = -1)){
C <- v * (p * C[(1+f7):(i+1+f7)] +
(1 - p)* C[(0+f7):(i+f7)])
}
C
}
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