GeometricBrownianMotion: Simulate paths from a Arithmetic or Geometric Brownian Motion

In fExpressCertificates: Structured Products Valuation for ExpressCertificates/Autocallables

Description

Simulate one or more paths for an Arithmetic Brownian Motion B(t) or for a Geometric Brownian Motion S(t) for 0 ≤ t ≤ T using grid points (i.e. Euler scheme).

Usage

BM(S0, mu=0, sigma=1, T, N)
GBM(S0, mu, sigma, T, N)
GeometricBrownianMotionMatrix(S0, mu, sigma, T, mc.loops, N)

Arguments

S0	start value of the Arithmetic/Geometric Brownian Motion, i.e. S(0)=S0 or B(0) = S0
mu	the drift parameter of the Brownian Motion
sigma	the annualized volatility of the underlying security, a numeric value; e.g. 0.3 means 30% volatility pa.
T	time
mc.loops	number of Monte Carlo price paths
N	number of grid points in price path

Value

a vector of length N+1 with simulated asset prices at (i * T/N), i=0,...,N.

Author(s)

Stefan Wilhelm [e-mail]

References

Iacus, Stefan M. (2008). Simulation and Inference for Stochastic Differential Equations: With R Examples Springer

Examples

# Simulate three trajectories of the Geometric Brownian Motion S(t)
T        <- 1
mc.steps <- 100
dt       <- T/mc.steps
t        <- seq(0, T, by=dt)
S_t      <- GBM(S0=100, mu=0.05, sigma=0.3, T=T, N=mc.steps)
plot(t, S_t, type="l", main="Sample paths of the Geometric Brownian Motion")
for (i in 1:2) {
 S_t      <- GBM(S0=100, mu=0.05, sigma=0.3, T=T, N=mc.steps)
 lines(t, S_t, type="l")
}

Example output

Loading required package: mvtnorm
Loading required package: tmvtnorm
Loading required package: Matrix
Loading required package: stats4
Loading required package: gmm
Loading required package: sandwich
Loading required package: fCertificates
Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries


Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: [e-mail]
Loading required package: fOptions


Rmetrics Package fOptions
Pricing and Evaluating Basic Options
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: [e-mail]
Loading required package: fExoticOptions

fExpressCertificates documentation built on May 2, 2019, 11:02 a.m.