The Hull-White Model under Volatility Uncertainty
Abstract
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.
Cite
@article{arxiv.1808.03463,
title = {The Hull-White Model under Volatility Uncertainty},
author = {Julian Hölzermann},
journal= {arXiv preprint arXiv:1808.03463},
year = {2021}
}
Comments
rewrote/restructured the paper while main results remain unchanged; left out the part about drift uncertainty; included a section about yield curve fitting and a multifactor extension