R Monte Carlo Simulation Tutorial

# [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()

#!/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

sbatch stock-price.sbatch