38 lines
1.5 KiB
R
38 lines
1.5 KiB
R
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# European put option pricing using characteristic function
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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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#' European put option pricing using characteristic function
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#'
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#' As seen in Epps (2009)
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#' @param char.fn Characteristic function of the price level at expiry time
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#' @param strikeprice Strike price, relative to a unit stock price
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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 ... Parameters of the characteristic function
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#' @param int.bounds Integration bounds for the integrate() method used. Defaults to infinite bounds.
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#' @return European put option price
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#'
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#' @author Francois Pelletier
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putEpps <- function(char.fn,strikeprice,eval.time,expiry.time,rate,...,int.bounds=c(-Inf,Inf))
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{
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# function to integrate (zhi)
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zhi <- function(x,char.fn,strikeprice,eval.time,expiry.time,rate,...)
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{
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Re(strikeprice^{-1i*x} *
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char.fn(x,strikeprice,eval.time,expiry.time,rate,...) /
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(x*(1i+x)))
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}
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# function to integrate with strike price as first parameter
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integrate.K <- function(strikeprice,zhi,int.bounds,eval.time,expiry.time,rate,...)
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{
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exp(-rate*(expiry.time-eval.time)) *
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strikeprice *
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(.5 - integrate(zhi,int.bounds[1],int.bounds[2],strikeprice,eval.time,expiry.time,rate,...)$value / (2*pi))
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}
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mclapply(as.vector(strikeprice),integrate.K,zhi,int.bounds,eval.time,expiry.time,rate,...)
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}
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