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We focus on extending existing short-rate models, enabling control of thegenerated implied volatility while preserving analyticity. We achieve this goalby applying the Randomized Affine Diffusion (RAnD) method to the class ofshort-rate processes under the Heath-Jarrow-Morton framework. Underarbitrage-free conditions, the model parameters can be exogenously stochastic,thus facilitating additional degrees of freedom that enhance the calibrationprocedure. We show that with the randomized short-rate models, the shapes ofimplied volatility can be controlled and significantly improve the quality ofthe model calibration, even for standard 1D variants. In particular, weillustrate that randomization applied to the Hull-White model leads to dynamicsof the local volatility type, with the prices for standard volatility-sensitivederivatives explicitly available. The randomized Hull-White (rHW) model offersan almost perfect calibration fit to the swaption implied volatilities.

Randomization of Short-Rate Models, Analytic Pricing and Flexibility in Controlling Implied Volatilities