R Monte Carlo Simulation Tutorial

In this tutorial, we will run an R script. The R script runs a Monte Carlo simulation to estimate the path of a stock price using the Geometric Brownian stochastic process.

R Script

# [stock-price.R]

GeometricBrownian<-function()

{

  paths<-10

  count<-5000

  interval<-5/count

  mean<-0.06

  sigma<-0.3

  sample<-matrix(0,nrow=(count+1),ncol=paths)

  for(i in 1:paths)

    {

      sample[1,i]<-100

      for(j in 2:(count+1))

      {

        #Expression for Geometric Brownian Motion

        sample[j,i]<-sample[j-1,i]*exp(interval*(mean-((sigma)^2)/2)+((interval)^.5)*rnorm(1)*sigma)

      }

    }

    cat("E[W(2)] = ",mean(sample[2001,]),"\n")

    cat("E[W(5)] = ",mean(sample[5001,]),"\n")

    #pdf <- paste("result_", tid, ".pdf", sep = "")

    #pdf(file="out.pdf")

    hist(sample)

    matplot(sample,main="Geometric Brownian",xlab="Time",ylab="Path",type="l")

    dev.off()

}

GeometricBrownian()

Slurm Script

#!/bin/bash

#

# [ stock-price.sbatch  ]

#

# This slurm submission script runs a Monte Carlo simulation to 

# estimate the path of a stock price using the geometric

# Brownian motion stochastic process.

#

# -----------------------------------------------------------------------------

#

# slurm job scheduler directives begin with "#SBATCH"

#

#SBATCH --job-name=spJob                    # Job name

#SBATCH --time=00:10:00                     # Wall-clock time limit for this job

#SBATCH --mem=4G                            # Request 4G RAM

#SBATCH --mail-type=END,FAIL                # email user when job ENDs or FAILs

#SBATCH --mail-user=you@stern.nyu.edu       # email TO

#SBATCH --output=helloJob%j.out             # write output; "%j" = job ID

#SBATCH --partition=test                    # test partition max time 1hr

#

#

# **** Note: It is always advantages to specify conservative values

#       for run time and memory. Jobs requesting fewer resources are more

#       likely to be scheduled before jobs requesting more resources.

#

# --------------------

# How to submit job to Stern grid

#

# sbatch  --array=5-15:5 fitspline.embedded-sbatch.sh

# --------------------------------------------------------------------

# Select stat package and version to use

  module  purge

  module  load  R/4.0.2

# R CMD BATCH --slave fitspline.R fitspline.$SLURM_JOBID.Rout

#  R CMD BATCH --slave fitspline.R fitspline.$SLURM_TASK_PID.Rout

  R CMD BATCH stock-price.R

To execute this script, run the following command:

sbatch stock-price.sbatch