Especially in the insurance industry interest rate models play a crucial role, e.g. to calculate the insurance company’s liabilities, performance scenarios or risk measures. A prominant candidate is the 2-Additive-Factor Gaussian Model (Gauss2++ model)—in a different representation also known as the 2-Factor Hull-White model. In this paper, we propose a framework to estimate the model such that it can be applied under the risk neutral and the real world measure in a consistent manner. We first show that any time-dependent function can be used to specify the change of measure without loosing the analytic tractability of, e.g. zero-coupon bond prices in both worlds. We further propose two candidates, which are easy to calibrate: a step and a linear function. They represent two variants of our framework and distinguish between a short and a long term risk premium, which allows to regularize the interest rates in the long horizon. We apply both variants to historical data and show that they indeed produce realistic and much more stable long term interest rate forecast than the usage of a constant function, which is a popular choice in the industry. This stability over time would translate to performance scenarios of, e.g. interest rate sensitive fonds and risk measures.

尤其是在保险行业，利率模型起着至关重要的作用，例如，计算保险公司的负债，业绩情景或风险衡量标准。突出的候选对象是2加因子因数高斯模型（Gauss2 ++模型），在另一种表示形式中也称为2因数赫尔怀特模型。在本文中，我们提出了一个框架来估算模型，以便可以以一致的方式在风险中性和现实度量下应用该模型。我们首先表明，任何与时间相关的函数都可以用于指定度量的变化，而不会降低分析的可处理性，例如，两个世界中的零息债券价格。我们进一步提出了两个易于校准的候选：阶跃和线性函数。它们代表了我们框架的两个变体，并区分了短期和长期风险溢价，从而使长期利率得以规范。我们将这两种变体应用于历史数据，并表明它们确实产生了比使用常数函数更为现实和稳定的长期利率预测，而常数函数的使用在行业中是一个普遍的选择。