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

TL;DR

This paper introduces a randomized extension of short-rate models within the Heath-Jarrow-Morton framework, allowing enhanced control over implied volatility and improved calibration, especially for the Hull-White model.

Contribution

It develops the Randomized Affine Diffusion method for short-rate models, enabling stochastic parameters and better implied volatility control while maintaining analyticity.

Findings

Randomized models improve calibration quality.

Randomization leads to local volatility-like dynamics.

The randomized Hull-White model fits swaption volatilities almost perfectly.

Abstract

We focus on extending existing short-rate models, enabling control of the generated implied volatility while preserving analyticity. We achieve this goal by applying the Randomized Affine Diffusion (RAnD) method to the class of short-rate processes under the Heath-Jarrow-Morton framework. Under arbitrage-free conditions, the model parameters can be exogenously stochastic, thus facilitating additional degrees of freedom that enhance the calibration procedure. We show that with the randomized short-rate models, the shapes of implied volatility can be controlled and significantly improve the quality of the model calibration, even for standard 1D variants. In particular, we illustrate that randomization applied to the Hull-White model leads to dynamics of the local volatility type, with the prices for standard volatility-sensitive derivatives explicitly available. The randomized Hull-White (rHW) model offers an almost perfect calibration fit to the swaption implied volatilities.