波动率不确定性下的Hull-White模型
The Hull-White Model under Volatility Uncertainty
摘要：
本文研究了存在波动不确定性的利率期限结构的Hull-White模型。关于波动率的不确定性由一组信念表示，这自然会导致一个次线性期望和一个G-布朗运动。在这种情况下的主要问题是如何找到一个无仲裁的期限结构。这个问题是至关重要的，因为我们可以证明，经典的方法，鞅模型，不存在波动的不确定性。因此，我们需要调整模型，以找到一个无套利的期限结构。由此产生的期限结构是仿射的短期利率和调整因子。虽然调整改变了模型的结构，但在拟合收益率曲线后，仍然与传统的Hull-White模型保持一致。此外，我们将模型和结果扩展到多因素版本，由多个风险因素驱动。
英文摘要：
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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