应对负短期利率
Coping with Negative Short-Rates
摘要：
我们讨论了一个简单的推广的Ho和Lee模型与一般的时间依赖性漂移：1）我们计算债券价格解析; 2）收益率曲线是敏感的，渐近收益率是积极的;和3）我们的分析解决方案提供了一个干净和简单的方式分离波动性的漂移在短期利率过程。我们的扩展相当于为底层的布朗运动（与短速率相反）引入一个或两个反射障碍，这允许具有更现实的时间依赖性漂移（与恒定漂移相反）。在我们的模型中，频谱--或者粗略地说，对债券和其他索赔价格有贡献的短期利率值的集合--是离散的和正的。我们讨论了如何使用经验产量数据来校准我们的模型，通过拟合三个参数，然后读出随时间变化的漂移。
英文摘要：
We discuss a simple extension of the Ho and Lee model with generic time-dependent drift in which: 1) we compute bond prices analytically; 2) the yield curve is sensible and the asymptotic yield is positive; and 3) our analytical solution provides a clean and simple way of separating volatility from the drift in the short-rate process. Our extension amounts to introducing one or two reflecting barriers for the underlying Brownian motion (as opposed to the short-rate), which allows to have more realistic time-dependent drift (as opposed to constant drift). In our model the spectrum -- or, roughly, the set of short-rate values contributing to bond and other claim prices -- is discrete and positive. We discuss how to calibrate our model using empirical yield data by fitting three parameters and then read off the time-dependent drift.
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