Hi donal, Hull-White cannot match the skew. Generally for short-tenor swaptions the smile implied by Hull-White is closed to normal, and it tilts a bit for longer tenor, but you cannot manipulate it by playing with the model parameters. Well, technically you could for long-tenor swaptions, by playing with the speed of mean reversion, but you shouldn't attempt to do that at home This is a price you have to pay for having closed form formulas for zero-coupon bonds. There are two ways out of this: either use out-of-model adjusters (search for Hagan adjusters) or use a model that has smile. The two models that have smile and also closed-form zero-coupon bonds are the quasi-Gaussian model (a.k.a. Cheyette) and the quadratic Gaussian model. The first is a straightforward generalization of HW, but you pay a price in the number of state variables. The second is again a generalization of HW, where you add a quadratic term, as the name implies. However, it requires some thougth to get familiar with. Of course, there are models without closed-form ZCB; you calculate the ZCB's on the grid using backward induction. Best,V.