44 lines
1.4 KiB
R
44 lines
1.4 KiB
R
# Damped characteristic function of the call option log-price
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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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#' Damped characteristic function of the call option log-price
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#' @param u Transform variate
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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 moneyness Boolean for moneyness of call option
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#' (TRUE if strike price is lower than stock price)
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#' @return Characteristic function value
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#' @export dampedcfcallCarrMadan
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#' @author Francois Pelletier
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dampedcfcallCarrMadan <- function(u,char.fn,eval.time,expiry.time,rate,alpha,...,moneyness=TRUE)
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{
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if(moneyness)
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{
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return(exp(-rate*(expiry.time-eval.time))*
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char.fn(u-1i*(alpha+1),expiry.time-eval.time,...) /
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(alpha^2+alpha-u^2+1i*u*(2*alpha+1)))
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}
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else
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{
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auxiliairyf <- function(u,char.fn,eval.time,expiry.time,rate,alpha,...)
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{
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exp(-rate*(expiry.time-eval.time))*
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(1/(1+1i*u)-exp(rate*(expiry.time-eval.time))/
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(1i*u)-char.fn(u-1i,expiry.time-eval.time,...)/(u^2-1i*u))
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}
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return((auxiliairyf(u-1i*alpha,char.fn,eval.time,expiry.time,rate,alpha,...)-
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auxiliairyf(u+1i*alpha,char.fn,eval.time,expiry.time,rate,alpha,...))/2)
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}
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}
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