AbstractIn this article, we propose a simple interest rate model, which can well accom-modate swaption smiles, while recovering market prices of CMS swap spreads. Themodel is based on a (possibly multi-factor) Gaussian short rate model coupled withparameter uncertainty. Examples of calibration to real market data will be presentedas well as the pricing of some typical CMS-based derivatives. 1 Introduction Swap rate dependent derivatives have become increasingly popular in the interest ratemarket. Typical examples are the CMS spreads and CMS spread options, whose payofisare based on the difierence between long and short maturities swap rates. Such payofisare usually embedded in swaps, which may be cancelled due to Bermudan-style callabilityfeatures or to TARN-style conditions.To be correctly priced, such derivatives need a model that incorporates at once themarket swaption volatilities of all the relevant swap rates (both at-the-money and away-from-the-money) consistently with a realistic form for their correlation term structure.Swaption volatilities are usually quoted in the market by means of the SABR functionalform, see Hagan et al. (2002), implicitly assuming a difierent (and independent) stochasticvolatility model for each difierent swap rate. Motivating this practice on the basis of aproper market model is still an issue to be addressed. On the other hand, one can simplyregard the swaption smile as a market input to which to calibrate one’s favorite interestrate model. In this case, an efiective and rather straightforward solution is obtained bycoupling a short-rate model with parameter uncertainty in the spirit of Brigo, Mercurio1