1
$\begingroup$

I am trying to use Hull White Model to price a zero coupon bond by Monte Carlo Simulation. The basic idea is under this equation:enter image description here

Under Hull White Model, I want to generate every short rate (r) and integrate them to get the price. Based on the HW model, the dr(t) process includes a v(t) term as follow. I don't quite understand how to simulate thee v(t) process under Monte Carlo, can anyone help? enter image description here

Improve this question
$\endgroup$

1 Answer 1

Reset to default
3
$\begingroup$

You do not model $v(t)$ by Monte-Carlo! As your excerpt explains $\phi(t)$ is a deterministic function of the initial yield curve and accordingly $v(t)$ is deterministic as well. Two further remarks: (i) You should not base the model on $v(t)$ but on an integrated $v(t)$, since this only involves the first derivative of the forward rates. (ii) You should not model $r(t)$ and then integrate to find $\int{r(t)}$ but model both at the same time as a joint Gaussian process.

All these issues are clearly (and in detail) explained in the standard reference Glasserman (Chapter 3.3 Gaussian short rate models).

Improve this answer
$\endgroup$
4
  • $\begingroup$ Question please: why do we need to simulate $\int{r(t)}$ for discount factors? Can we not use $A*exp(-B*r(t))$, once we have simulated $r(t)$. $\endgroup$
    – InnocentR
    Oct 27, 2019 at 18:35
  • $\begingroup$ Why don't you post this as a question? $\endgroup$
    – g g
    Oct 27, 2019 at 21:05
  • $\begingroup$ I had asked earlier but sadly not much help: quant.stackexchange.com/questions/43101/… $\endgroup$
    – InnocentR
    Oct 27, 2019 at 21:08
  • $\begingroup$ "You should not model r(t) and then integrate to find ∫r(t) but model both at the same time as a joint Gaussian process." - This requires further elaboration. Linking to Glasserman is not an answer, especially in light of the fact, that this is a 50€ book. $\endgroup$
    – Martin Erhardt
    Jul 1 at 10:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.