fastGBM: Generating Geometric Brownian motion

In LSMonteCarlo: American options pricing with Least Squares Monte Carlo method

Description

Quick Generating Geometric Brownian motion avoiding unnecessary loops using the cumsum function. Technical function implemented in the pricing functions of the package.

Usage

fastGBM(Spot = 1, sigma = 0.2, n = 1000, m = 365, r = 0.06, dr = 0, mT = 1)

Arguments

Spot	Spot price of the underlying asset (e.g. stock).
sigma	Volatility of the underlying asset.
n	Number of paths simulated.
m	Number of time steps in the simulation.
r	Interest rate of the numeraire currency (e.g. EUR).
dr	Dividend rate of the underlying asset.
mT	Maturity time (years).

Value

Table with paths generated (each row is a path, class "matrix")

Author(s)

Mikhail A. Beketov

See Also

Functions: AmerPutLSM, AmerPutLSM_AV, AmerPutLSM_CV, AsianAmerPutLSM, QuantoAmerPutLSM, and QuantoAmerPutLSM_AV.

Examples

fastGBM(n=10, m=5)
matplot(t(fastGBM(n=100, m=100)), type="l") # matrix transpose by "t()"

Example output

Loading required package: mvtnorm
Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries
           [,1]      [,2]      [,3]      [,4]      [,5]
 [1,] 1.0293330 1.2681723 1.4612960 1.3824041 1.2993430
 [2,] 1.0701101 1.1187611 1.0774588 1.2144478 1.2754968
 [3,] 0.9531196 0.8699422 0.9712432 1.1640761 1.1840269
 [4,] 1.0000492 0.9814904 1.1057886 1.1607309 0.9654719
 [5,] 1.0538666 0.9814689 0.9258868 0.8632822 0.8131753
 [6,] 1.0156393 0.8217586 0.8323415 0.6688556 0.7598782
 [7,] 0.9993939 0.8595950 0.9019661 1.0945507 1.1612638
 [8,] 1.1074479 1.0370886 1.0623639 1.2599998 1.1451754
 [9,] 1.0567969 1.1465284 1.1234061 1.2959196 1.4313935
[10,] 1.0924809 1.0374408 1.0019155 0.8947288 0.9881024

LSMonteCarlo documentation built on May 2, 2019, 8:55 a.m.