Hull White Process MonteCarlo

[LE Ruiqi]

Hi All,
I found that there is no dircet way to monte carlo the sequence of short rate for HW model in quantlib,
remember that r =x + Phi (where r is short rate, x is the Ulenbeck Process, Phi is the parameter fitting )
then :
1)I monte carlo the Ulenbeck Process at first, where x + = path.drift()[i] + path.diffusion()[i]; ( but i found that in quantlib asset * =Exp(drift()[i]+diffusion()[i]), am I wrong????  
2) add the Phi to x, then derive the r sequence;

but unfortunately, i use the short rate r to price the put option on zero bond, and found that the relative price error is about 10%, which is much high.
so can someone tell me how to monte carlo the short rate process?

thx

Ruiqi

 

[Luigi Ballabio-2]

On 2004.06.24 12:25, LE Ruiqi wrote:
> I found that there is no dircet way to monte carlo the sequence of
> short rate for HW model in quantlib,
> remember that r =x + Phi (where r is short rate, x is the Ulenbeck
> Process, Phi is the parameter fitting )
> then :
> 1)I monte carlo the Ulenbeck Process at first, where x + =
> path.drift()[i] + path.diffusion()[i]; ( but i found that in quantlib
> asset * =Exp(drift()[i]+diffusion()[i]), am I wrong????

No, you are right. The difference is due to the fact that for assets,  
the variable whose diffusion is modeled is log(x)--hence the  
exponential.

As for the main question, i.e.,

> can someone tell me how to monte carlo the short rate process?

I haven't an answer at this time...

Later,
        Luigi