Before revision:  Within this framework, it is shown how to characterize the whole term structurewithout admitting arbitrage. The pricing of zero-coupon bonds in such a setting differs substantially from traditional models, since the prices need to be chosen in a different way in order to exclude arbitrage .
After revision:  The main question in this setting is how to find an arbitrage-free term structure. This question is crucial, since we can show that the classical approach, martingale modeling, does not work in the presence of volatility uncertainty. Therefore, we need to adjust the model in order to find an arbitrage-free term structure. The resulting term structure is affine with respect to the short rate and the adjustment factor. Although the adjustment changes the structure of the model, it is still consistent with the traditional Hull-White model after fitting the yield curve. In addition, we extend the model and the results to a multifactor version, driven by multiple risk factors .