Coping With Negative Short Rates

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 us 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 reading off the time‐dependent drift.