#Creating a Single Random walk

#first need to specify parameters
S0=100   #starting stock price
mu=.08   #drift
s=.3    #volatility
T=1   #time frame in years

n=252   #number of subintervals
dt=T/n   #timestep

walk=double(n+1)
walk[1]=S0

for (j in 2:(n+1)){
     walk[j]=walk[j-1]+walk[j-1]*mu*dt+walk[j-1]*s*rnorm(1,mean=0,sd=sqrt(dt))}

plot(walk,type='l')

dailymusannualized=double(n)
for (i in 1:n){
dailymusannualized[i]=log(walk[i+1]/walk[i])*n/T}

mean(dailymusannualized)
sterr=sd(dailymusannualized)/sqrt(n)
sterr

volatility=sd(dailymusannualized*sqrt(dt))
volatility