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Mastering R for Quantitative Finance by Edina Berlinger, Ferenc Illés, Milán Badics, Ádám Banai, Gergely Daróczi, Barbara Dömötör, Gergely Gabler, Dániel Havran, Péter Juhász, István Margitai, Balázs Márkus, Péter Medvegyev, Julia Molnár, Balázs Árpád Szűcs, Ágnes Tuza, Tamás Vadász, Kata Váradi, Ágnes Vidovics-Dancs

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The life of a Double-no-touch option – a simulation

How has the DNT price been evolving during the second quarter of 2014? We have the open-high-low-close type time series with five minute frequency for AUDUSD, so we know all the extreme prices:

d <- read.table("audusd.csv", colClasses = c("character", rep("numeric",5)), sep = ";", header = TRUE)
underlying <- as.vector(t(d[, 2:5]))
t <- rep( d[,6], each = 4)
n <- length(t)
option_price <- rep(0, n)

for (i in 1:n) {
  option_price[i] <- dnt1(S = underlying[i], K = 1000000, U = 0.9600, L = 0.9200, sigma = 0.06, T = t[i]/(60*24*365), r = 0.0025, b = -0.0250)
}
a <- min(option_price)
b <- max(option_price)
option_price_transformed = (option_price - a) * 0.03 / (b - a) + 0.92

par(mar = c(6, 3, 3, 5)) ...

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