https://github.com/cran/fOptions
Tip revision: 9c58bb98a62fa8226a1f41c6fb1f98485b101250 authored by Rmetrics Core Team on 08 August 1977, 00:00:00 UTC
version 270.74
version 270.74
Tip revision: 9c58bb9
runit.MonteCarloOptions.R
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
# Copyrights (C)
# for this R-port:
# 1999 - 2007, Diethelm Wuertz, GPL
# Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
# info@rmetrics.org
# www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
# see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
# see Rmetrics's copyright file
################################################################################
# FUNCTION: DESCRIPTION:
# MonteCarloOption Valuate Options by Monte Carlo Simulation
################################################################################
test.MonteCarloOption <-
function()
{
# How to perform a Monte Carlo Simulation?
# RVs:
RNGkind(kind = "Marsaglia-Multicarry", normal.kind = "Inversion")
set.seed(4711, kind = "Marsaglia-Multicarry")
# First Step:
# Write a function to generate the option's innovations.
# Use scrambled normal Sobol numbers:
sobolInnovations = function(mcSteps, pathLength, init, ...) {
# Create Normal Sobol Innovations:
innovations = rnorm.sobol(mcSteps, pathLength, init, ...)
# Return Value:
innovations
}
# Second Step:
# Write a function to generate the option's price paths.
# Use a Wiener path:
wienerPath = function(eps) {
# Note, the option parameters must be globally defined!
# Generate the Paths:
path = (b-sigma*sigma/2)*delta.t + sigma*sqrt(delta.t)*eps
# Return Value:
path
}
# Third Step:
# Write a function for the option's payoff
# Example 1: use the payoff for a plain Vanilla Call or Put:
plainVanillaPayoff = function(path) {
# Note, the option parameters must be globally defined!
# Compute the Call/Put Payoff Value:
ST = S*exp(sum(path))
if (TypeFlag == "c") payoff = exp(-r*Time)*max(ST-X, 0)
if (TypeFlag == "p") payoff = exp(-r*Time)*max(0, X-ST)
# Return Value:
payoff
}
# Example 2: use the payoff for an arithmetic Asian Call or Put:
arithmeticAsianPayoff = function(path) {
# Note, the option parameters must be globally defined!
# Compute the Call/Put Payoff Value:
SM = mean(S*exp(cumsum(path)))
if (TypeFlag == "c") payoff = exp(-r*Time)*max(SM-X, 0)
if (TypeFlag == "p") payoff = exp(-r*Time)*max(0, X-SM)
# Return Value:
payoff
}
# Final Step:
# Set Global Parameters for the plain Vanilla / arithmetic Asian Options:
TypeFlag <<- "c"; S <<- 100; X <<- 100
Time <<- 1/12; sigma <<- 0.4; r <<- 0.10; b <<- 0.1
# Do the Asian Simulation with scrambled random numbers:
mc = MonteCarloOption(delta.t = 1/360, pathLength = 30, mcSteps = 5000,
mcLoops = 50, init = TRUE, innovations.gen = sobolInnovations,
path.gen = wienerPath, payoff.calc = arithmeticAsianPayoff,
antithetic = TRUE, standardization = FALSE, trace = TRUE,
scrambling = 2, seed = 4711)
# Plot the MC Iteration Path:
par(mfrow = c(1, 1))
mcPrice = cumsum(mc)/(1:length(mc))
plot(mcPrice, type = "l", main = "Arithmetic Asian Option",
xlab = "Monte Carlo Loops", ylab = "Option Price")
# Compare with Turnbull-Wakeman Approximation:
# ... requires(fExoticOptions)
# TW = TurnbullWakemanAsianApproxOption(TypeFlag = "c", S = 100, SA = 100,
# X = 100, Time = 1/12, time = 1/12, tau = 0 , r = 0.1, b = 0.1,
# sigma = 0.4)$price
# print(TW)
TW = 2.859122
abline(h = TW, col = 2)
# Return Value:
return()
}
################################################################################