58 lines
2 KiB
R
58 lines
2 KiB
R
# Call price using the Carr-Madan damping parameter and FFT
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#
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# Author: Francois Pelletier
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#
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# LGPL 3.0
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###############################################################################
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#' Call price using the Carr-Madan damping parameter and FFT
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#' @param strikeprice Vector of strike prices, relative to a unit stock price
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#' @param char.fn Characteristic function of the log-price process
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#' @param eval.time Evaluation time
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#' @param expiry.time Expiry time
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#' @param rate Continuously compounded interest rate (force of interest)
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#' @param alpha Damping parameter
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#' @param ... Parameters of the characteristic function
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#' @param fft.control Control parameters list for the FFT discretization
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#' @return A European call option price vector
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#' @export callCarrMadan
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#' @author Francois Pelletier
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callCarrMadan <- function(strikeprice,char.fn,eval.time,expiry.time,rate,alpha,
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...,fft.control=list(N=2^14,eta=.1))
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{
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# Determine moneyness
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moneyness <- strikeprice < 1
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# Discretization step for Fourier transform
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lambda <- lambda <- (2*pi) / (fft.control$N*fft.control$eta)
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# Evaluation points of the damped characteristic function of the call option log-price
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u <- seq(0,(fft.control$N-1)*fft.control$eta,fft.control$eta)
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# Upper bound
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b <- (fft.control$N * lambda)/2
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# Vector of indices
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jvec <- 1:fft.control$N
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# Simpson's hypothesis
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simpsonh <- ((dampedcfcallCarrMadan(u,char.fn,eval.time,expiry.time,rate,alpha,...,moneyness)*
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exp(1i*u*b)*fft.control$eta)/3)*
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(3+(-1)^jvec+((jvec-1)==0))
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# Log-price vector
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ku <- seq(-b,(fft.control$N-1)*lambda-b,lambda)
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# Log-price of the call option vector
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if(moneyness)
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{
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callvec <- Re((exp(-alpha*ku)*fft(simpsonh))/pi)
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}
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else
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{
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callvec <- fft(simpsonh)/(sinh(alpha*ku)*pi)
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}
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# Price vector
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Ku <- exp(ku)
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# Index to select subset of prices in the strikeprice vector
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Kindex <- Ku>=(min(strikeprice)-1) & Ku<=(max(strikeprice)+1)
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# We use a smooth spline to get the prices for the strikeprice vector
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sp0 <- smooth.spline(x=Ku[indice],y=callvec[indice])
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predict(sp0,strikeprice)$y
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}
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