# Ho-Lee Model Calibration: theta becomes smaller

This question is regarding the Ho-Lee model:

$$dr_t = \theta_tdt + \sigma dW_t$$

In discrete time, we can calibrate an interest rate binomial tree by finding $\theta$ in each period to match market price with the model price (expectations under the risk-neutral measure). However, every step I proceed to calibrate the next bond on the tree, the $\theta$ in the same period becomes smaller and smaller, because I'm using the calibrated interest rates for previous periods (not sure, please correct me if I'm wrong!).

My question is: what is the intuition/explanation of the $\theta$? Can we view it as the underlying "trend" of the interest rates since $\theta$ is the drift?

Thanks!

• Even when you're talking about standard models everyone knows, it's helpful to include the formulae in your question. – will Sep 4 '17 at 10:31
• You should now be able to answer your own question. Theta is the drift of the world forward rate. What are the prices you're calibrating to? Take a look at forward rate projections, and specifically what happens to dr/dt. – will Sep 5 '17 at 7:29
• @rxxxx: See whether the answer here is helpful for you. – Gordon Sep 5 '17 at 18:49