Re: Heston Monte Carlo Convergence

Posted by Lapin on Feb 15, 2008; 5:57pm
URL: http://quantlib.414.s1.nabble.com/Heston-Monte-Carlo-Convergence-tp5554p5557.html

To the actual questions, I would like to ask if someone has the experience of control variate in QL framework?
I would like to code delta and gamma control variate to reduce the error, btu if someone has an example, it would be great...

Cheers

Yomi wrote

Hi,

I have implemented a Monte Carlo engine for Heston, but the convergence is not so good in my view.
I am pricing a 5Y european down in put option.
The calibration is almost perfect (less than 1bps in average), but the convergence of the simulation is quite poor.
 
As you can see in the following table, the price swings if I increase the number of steps by year.
 
Steps by year Price
4 14.90%
10 14.12%
20 14.13%
30 13.39%
50 13.58%
100 14.67%
200 14.17%
300 13.71%
350 13.87%
400 14.25%

Since it is European, the convergence should be quick and the result should not depend so much on the Time steps by year.
I have enclosed the calibrated parameters of Heston.
 
Name Heston
Spot 3730.65
Integration 64
V0 7.76%
Kappa 188.03%
Theta 9.19%
Sigma 65.26%
Rho -95.49%

 
Do you know why there is no stability there? Is there any trick to make it stable?
 
I have also a question regarding the antithetical variables.
Is there anything else to do to use it of just say QL to draw them?

Cheers