Simulation Heston Model

[Fablepongiste]

Hello.
I need you help about the simulation of Heston Model.
I need to simulate this model using a Euler discetization scheme.
My problemes are :
Which values choose for the parameters. I found estimation on papers but i don't know if it's daily or annuals estimation ....
V0 = 0.1, k=2, theta = 0.01, sigma = 0.1, rho = 0.3, mu = ? 0.03 ?
I used a step of 0.02 = 1/50

I need to simulate daily assets values. I use the R code (also test in C++) below :

Heston<- function(mu, kapa, theta, sigma, rho)
{
v<-rep(0,100000)
x<-rep(0,100000)
v[1]<-0.01
x[1]<-5000
for (i in 2:100000)
{
normale1<-rnorm(1,0,1)
normale2<-rnorm(1,0,1)
normale3<-rho*normale1 + sqrt(1-rho*rho)*normale2
x<-x[i-1]*(1 + (mu/50) + sqrt(v[i-1]/50)*normale1)
v<-abs((kapa*theta/50) + (1-(kapa/50))*v[i-1] + sigma*sqrt(v[i-1]/50)*normale3)
}
x
}

Heston(0.0001,2,0.01,0.1,-0.3)

I also try to simulate returns (using ito lemme) but resultts were also very bad.

Fabien

 

[Bastian Gross]

for (i in 2:100000)
{
normale1<-rnorm(1,0,1)
normale2<-rnorm(1,0,1)
normale3<-rho*normale1 + sqrt(1-rho*rho)*normale2
x<-x[i-1]*(1 + (mu/50) + sqrt(v[i-1]/50)*normale1)
v<-abs((kapa*theta/50) + (1-(kapa/50))*v[i-1] + sigma*sqrt(v[i-1]/50)*normale3)
}

I also try to simulate returns (using ito lemme) but resultts were also very bad.

Fabien

Hallo Fabien,

why do you want to simulate an Heston-Price?
Do the closed-form-estimation!
But in answer of your question:
You need 2 "for-loops", one in cause of the time-discretization, and the other one to simulate Monte Carlo.
In your code you should get some results, that differs from time to time.


Bastian

 

[Andy Nguyen]

Here is a detailed paper with mathematica code to calculate put, call
Stochastic Volatility - QuantNetwork - Financial Engineering Forum

 

[shinichi]

It's very famous that Euler (and even Milstein) doesn't converge for Heston. You should try Andersen from BofA or Smith from Santander.

 

[Curious]

Hi,
I need to simulate an heston model too.. if i can have your help??
i will simulate the equations on the article "closed-form solution for options with stochastic volatility with applications to bond and currency options" by Heston.. page328/331
thanks a lot!!