I'm working on implementing the two factor HW model using a monte carlo simulation. I also need to model two interest rate curves simultaneously, which needs the correlation between the two curves to be incorporated. Does anyone have any reading suggestions or papers which deals with this problem?

I'm wondering if you ever found anything on the this subject. I am considering doing a very similar thing and would love to hear some feedback (or trade ideas).

I have successfully implemented this via monte carlo on 4 curves. I did it using Brigo/Mercurio, which is simply an awesome book. Don't use the formulas from Hull, they have a typo, and I learned it the hard way. Brigo and Mercurio provide a nice section on the model, on calibration, and even some advice on MCS (time step, discretization, etc).Good luck

Since the HW2 can be done with tree, what's the advantage with MC?

Hi Stylz,I have also followed the methodology described in Brigo/Mercury for Hull White Monte Carlo simulation for one factor. I have implemented it in matlab and then tried to price caps to compare to the theoretical values, but I am getting bad results... Could you please tell me which pages of the book did you use for your implementation? Do you know some paper concerning this matter?Thank you very much

Brigo and Mercurio discuss how you could simulate 2 curves simultaneously using G2++ in page 610 2nd. I guess you could extend that for HW. Are the rates curves that you want to simulate on the same currency ? If not then the calibration will be an issue.

acasimiro,i think i just used Hull for this one, although brigo and mercurio cover this too.i think the main idea to get this one right is:1. computing short rate drift requires taking the derivative of instantaneous forward rates from initial zero curve. these are sensitive to interpolation type so try to use something with smooth forwards. when i first did this I used cubic splines on discount factors and the results converged. there are other methods too that should give you the required values.2. if your discretization is something like r(t+dt) = r(t) + (theta(t) - a * r) * dt + sigma * sqrt(dt) * N then keep your time steps small.3. How are you discounting back the payoffs? The way to do it is to use what I call "daisy chain" discounting. You must discount back at integral (0 to T) exp(-r(t)) dt. In practice, what this means is that in any given path you start with DF(0) = 1. Then, DF(dt) = DF(0) * exp(-R(0) * dt) where R(0) is the rate for time length dt expressed with continuous compounding as seen at time 0. NOTE R(0) <> the short rate at time 0. They should not be assumed equal. Similarly, DF(2 * dt) = DF(dt) * exp(-R(dt) * dt) where R(dt) is the rate for length dt expressed with continuous compounding as seen at time dt. And so on and so forth. The rate for length dt at any time step is solvable from the zero coupon bond price formulas. Cash flows in any path are then discounted using these discount factors. Actually, before you calcuate any caplet prices it is recommended to check that your model is arbitrage-free (i.e. that the average discount factors equal those computed analytically from the time-0 zero curve. If this check does not work you will never price anything correctly.4. Another good check is to compare the quantiles of your simulated rate with the formulas given is BM for the mean and variance of the simulated short rates.Good luck

Thanks for your great contribution. Could you please clarify the tip3? If you have any code available then will be great. Thanks