Hi,I'm trying to calibrate my hull-white model to the market.In the literature i read different ways to calibrate the model: calibration to the caplet volatilityor calibration to the swaption volatilities. What is the difference and what is better?Greetings,Richard

I first best-fit on the calibration basket to get (a,s) constant and then keep a to bootstrap and to get s(i).When I do that for a one-factor model and when I consider short-term underlying (6m in case of a caplet for example) the quality of the best-fit is poor and the graph of s(i) looks erratic.Do you get the same kind of resultats ?C

rplat,Neither caps or swaption is best. In principle you calibrate your model to the liquid products of the market that are relevent to your problem. Example 1:You are pricing an non-callable exotic which payoff is Libor based with coupon capped/floored.You will hedge yourself with swaps, caps and floors==> you will calibrate the drift on the yield curve and the volatility on the cap vols.The mean reversion will not impact your price.Example 2:You are pricing a bermudean swaptionYou will hedge yourself with swaptions so you calibrate on the relevent ones.Try to use the mean reversion to create some decorrelation.Example 3:You are pricing the exotic of example 1 but in a callable version.The 1F model is not adequate in this case as it will misprice the part of your hedge you could not use for the calibration.

Ok, thanks.I'm pricing a CMS cap based on an average 7-years swap rate, so i can use calibration to swaptions for this purpose.

Be carefull with CMS swaps/caps as well.Here only swaptions are relevent. But the CMS convexity is highly dependent on the swaption skew. Hull-White calibrated with ATM swaptions will undervalue the convexity.

So should i calibrate to the "skew-adjusted" volatility?

It is difficult to say: CMS convexity reflects prices of swaptions accross "all strikes". But you cannot use that many swaptions to calibrate this model.If I were you, I would :-price one simple (not averaged) CMS cap using static replication (or wahatever other good method - see related threads in the forum about CMS caps).-price the same CMS cap with your modelCompare the two to have an idea of how wrong your model can be.

Ok, thanks, that is a good idea.

Dear Clopinette,Thanks for your explanation, may i ask you some more questions?Now, i am trying to calculate the exposure of the swaps(many swaps), and i want to price these swaps now and also estimate their potenial exposure(some swaps started several years ago and some are forward swaps). The swaps maturity could last from one year to 30 years.If i want to use the hull white 1 factor model to simulate the interest rates, what kind of market instruments should i use to calibrate the parameters of the hull white 1 factor model? Caps/floors or swaption?If we use the caps for calibration(i suppose it is more reasonable than swaption,right?), what kind of caps should we use? Should we use the parameters from calibrating the short maturity caps to price the short maturity swaps, and also the same principle apply to those with long maturity?Even if so, still, Should i only use the at the money caps or i also need to use the quotes of in the money and out of the money?Is it sound to assume the alpha and sigma(mean reversion rate and volatility) to be constant? if it is more reasonable to make them function of time, then how should we estimate them?How to deal with the negative rates when simulating?So many questions!!! Hope to hear from you soon.Any comments is welcome.Thank you all in advance. QuoteOriginally posted by: Clopinetterplat,Neither caps or swaption is best. In principle you calibrate your model to the liquid products of the market that are relevent to your problem. Example 1:You are pricing an non-callable exotic which payoff is Libor based with coupon capped/floored.You will hedge yourself with swaps, caps and floors==> you will calibrate the drift on the yield curve and the volatility on the cap vols.The mean reversion will not impact your price.Example 2:You are pricing a bermudean swaptionYou will hedge yourself with swaptions so you calibrate on the relevent ones.Try to use the mean reversion to create some decorrelation.Example 3:You are pricing the exotic of example 1 but in a callable version.The 1F model is not adequate in this case as it will misprice the part of your hedge you could not use for the calibration.

(sorry, I answered to the rather old part of the thread below)