论文标题
Gauss2 ++模型 - 一致风险中性和现实世界校准的不同度量更改规格的比较
The Gauss2++ Model -- A Comparison of Different Measure Change Specifications for a Consistent Risk Neutral and Real World Calibration
论文作者
论文摘要
尤其是在保险行业中，利率模型起着至关重要的作用，例如计算保险公司的负债，绩效或风险措施。在不同表示形式中，一个倾向的候选者是2-辅助因素高斯模型（Gauss2 ++） - 也称为2因子壳壳模型。在本文中，我们提出了一个框架来估计模型，以便以一致的方式在风险中性和现实世界中应用。我们首先表明，任何渐进式和正方形的函数都可以用于指定度量的更改，而无需失去例如两个世界的零企业债券价格。我们进一步提出了两次依赖的候选者，这些候选者易于校准：一个步骤和线性函数。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，这使得可以在远距离的地平线上正规化利率。我们将这两个变体应用于历史数据，并表明它们确实产生了现实，更稳定的长期利率预测，而不是使用恒定功能。随着时间的推移，这种稳定将转化为例如利率敏感和风险措施。
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++) - 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 progressive and square-integrable 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 time dependent 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. This stability over time would translate to performance scenarios of e.g. interest rate sensitive fonds and risk measures.
