We construct an arbitrage-free short rate model under Knightian uncertainty about the volatility . The uncertainty  is represented by a set of priors , which naturally leads to a  G-Brownian motion. 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 .
We study the Hull-White model for the term structure of interest rates in the presence of volatility uncertainty . The uncertainty about the volatility is represented by a set of beliefs , which naturally leads to a sublinear expectation and a G-Brownian motion. 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 .
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construct an arbitrage-free short rate model under Knightian uncertainty about the volatility
study the Hull-White model for the term structure of interest rates in the presence of volatility uncertainty
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about the volatility
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priors
beliefs
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sublinear expectation and a
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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
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