HI everybody, In order to evaluate structures on CMS spread, we implemented the HW2F model (see Hull 5th edition page 571) calibrated on the underlying swaptions. The calibration parameters I get, are very high: I would expect a 1st mean-rev around 3% and a second one around 70% but we get a volatile 1st mean-rev between [0% - 25%] and a 2nd mean-rev up to 300%). Does anybody have any experience with this model? Regarding the EUR market, what are the ranges for the two mean-reversions and correl I would expect?Second point, did anybody implement the "2 Additive Factor Gaussian" model proposed by Brigo and Mercurio? What are the benefits and the drawbacks of this model versus the HW model?Thanks in advance,NY.

Hey, You're in luck - just built mine and have pretty much finished it apart from a small quirk in MC (whether this is actually an error or not remains to be seen!). Calibrating the HW2F as detailed in Hull 5th Edition;a 98.602%b 4.501%s1 0.693%s2 0.806%p 4.938%These params price 12 semi-annual EUR caps up to 20yrs with an average absolute error of 1bp. This model is pretty mental when it comes to finding a stable set of parameters. You can choose 2/3 of your parameters pretty much arbitraily and still get a fit using the remaining 3/2. What I'd suggest doing is pricing both caps and swaptions for calibration - caps are quite insensitive to correlation whereas swaptions have much greater sensitivity.Not build the G2++ as listed by B&M but it's on my to-do list if I can't take the closed-form approximation of a European swaption in that framework over to my HW2F (it's meant to be do-able, but in practice things can crop up...)Hope this helps, Jps. do you have closed-form swaption prices in HW2F you'd care to share (the analytic form, not the % prices I mean)? PM me if you wish

Thanks Mutley.I am sceptic with the outputs of the calibration as I don't know how to interpret the parameters. I am going to analyze more deeply the problem.Sorry but I do not have a closed-form formula for the swaption.NY.

No worries - how did you calibrate to the swaption prices then - did you use MC?EDIT:Not being one to thread-hijack often, but....As I run my MC simulation with volatile rates, the average money-market discount factor (i.e. ) I observe when I get to time T differs from the current time-T dcf I see from the zero rates. This effect increases with both time and volatility so I guess it means that it's some sort of convexity issue.I can price caps in MC and they converge on the analytic prices for caps, but when I price a portfolio of swaps through time they quickly move away from ATM. Is this correct?I can't find much/any literature on rolling a portfolio of anything through time using HW2F - if anyone has any pointers that would be terrific.J

I implemented the G2++ 2FHW formulation for this and have calibrated to swaptions. There is a semi-analytic formula for the swaptions calibration in Brigo/Mercurio which is not too bad to code. I also used my calibrated parameters in MCS and recovered my analytic prices. I find the performance of the model quite good depending on the set of instruments one uses. I calibrated to 1y through 10y expiries on 1y through 10y tails and got a good fit (the worst pricing error is around 4% on a total of 30 instruments). My parameters from a few weeks back were:alpha: .7beta: .062sigma: .024eta: .014Rho: -.786I'd be curious how these compare with others' findings out there.I did notice that the fit worsened when including very short expiries (e.g. 1m10y or even 3m10y) in the calibration set. But I find the model quite useful for my purpose which does not make use of such short term instruments.One other thing I am interested in is how the model performs for OTM strikes. I haven't had time to investigate this property yet.Hope it helps

Stylz, As you evolve your curve through time, do you get the same result as I've found (that the average bond price T-years in the future is less than the current T-year bond price)?Am going to build the HW2F swaption price and calibrate to swaptions as well as caps.J