Dear all,
I am using the following code for simulating Heston model. I am trying to
compare skewness with respect to different Rhos, but it doesn't seem to
work. Any body can tell me what is happening? I am using Euler-Maruyama
Monte Carlo. Here is my sample code. Any hints would be really appreciated.
theta=0.04
alpha=1.5
#delta=0.5
#rho=-0.9
n=100
m=1000
heston_sim<-function(rho,delta,m,mu){
s<-matrix(NA,n,m)
v<-matrix(NA,n,m)
for (j in 1:m){
for (i in 2:n) {
s[1,j]=2
v[1,j]=0.4
dt=1/100
zv<-rnorm(1)
zs<-rnorm(1)
zx<-rho*zv+sqrt(1-rho^2)*zs
w1<-zv*sqrt(dt)
w2<-zx*sqrt(dt)
s[i,j]=s[i-1,j]+(mu-0.5*max(v[i-1,j],0))*dt+sqrt(max(v[i-1,j],0))*w2
v[i,j]=v[i-1,j]+alpha*(theta-v[i-1,j])*dt+sqrt(max(v[i-1,j],0))*delta*w1
}
}
return(s)
}
s1<-heston_sim(-1,0.1,1000,0)
s2<-heston_sim(0,0.1,1000,0)
s3<-heston_sim(0.7,0.1,1000,0)
a1<-c(diff(s1,lag=1)*100)
a2<-c(diff(s2,lag=1)*100)
a3<-c(diff(s3,lag=1)*100)
plot(density(na.omit(a1),bw=0.5),main="",ylim=c(0,0.2))
lines(density(na.omit(a2),bw=0.5),col=2)
lines(density(na.omit(a3),,bw=0.5),col=3)
legend('topright',legend=c(expression(paste(rho,
"=--0.3")),expression(paste(rho, "=0")),expression(paste(rho,
"=0.5"))),col=1:3,lty=1)
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