> set.seed(100)

> n=1000

> x=cumsum(sample(c(-1,1),n,replace=TRUE))

> plot(x,type="l")

ARW:

Deltat= 10 %# time periods

T = 100 %Time(days)

N=T/deltat %# steps

For (t in 1:N)

{

rnorm(t,0,1)

}

1/19

arm.fun=function(x0,t,deltat,mu,sigma)

{

n=t/deltat

x.t=vector(length=n)

x.t[1]=x0+(mu*deltat+sigma*sqrt(deltat)*rnorm(1)) for (I in 2:n)

{

x.t[i]=x.t[i-1]+(mu*deltat+sigma*sqrt(deltat)*rnorm(1))

}

return(x.t)

}

1/26

end.fun=function(s0,t,mu,sigma,m){ end.s=vector(length=m) for (j in 1:m){ temp=gbm.fun(s0,t,mu,sigma) end.s[j]=temp[length(temp)]} return(end.s)}

gbm.fun=function(s0,t,mu,sigma){ deltat=1/365 n=t/deltat s.t=vector(length=n) deltas=s0*(mu*deltat+sigma*sqrt(deltat)*rnorm(1)) s.t[1]=deltas+s0 for (i in 2:n){ deltas=s.t[i-1]*(mu*deltat+sigma*sqrt(deltat)*rnorm(1)) s.t[i]=s.t[i-1]+deltas} return(s.t)}

Moving average:

n=length(prices)

Ma=vector(length=n)

Si=vector(length=n)

For (i in 1:n){ Si=prices[n-i]}

Return (si)

For (t in n-1:r) {

A=0

For (I in 0:n-1) {

A=a+si[t-i] }

Ma=a/n }

Return(ma)

Algorithm 5:

App.fun=function(n){

Z=vector(length=n)

For i in [1:n] {

Z=Z+runif(1) }

Z

2/1

bopm.fun=function(x0,u,d,n){ x=c( ) %collection…need to find relationship b/w # of nodes to put in vector form x[1] =x0 count=2 for (i in 1:n) { for (j in 0:i){ x[count]=x0 *u^j *d^(i-j) count=count+1} } return(x) }

2/15/15

ma.fun=function(prices,n)

{N=length(prices)

m=N-n+1 Ma=vector(length=m) for (i in 1:m) {Ma[i]=mean(prices[i:(i+n-1)])} return(Ma)}

risk.return=function(N,mu1,mu2,mu3,sig1,sig2,sig3,cov12,cov13,cov23){ for (i in 1:N){ sum=0 for (j in 1:3){ w[j]=runif(1) sum= sum + w[j] } for (j in 1:3){…