I was now reading a book on interest rate modelling, and I am having trouble picturing the practical issues of model calibration with the Ho-Lee model.
Apparently, one of the drawbacks of this model is the following:
The Ho-Lee model effectively has two parameters $-$ $r(0)$ and $\sigma_r$ $-$ with which one can attempt to fit the initial yield curve. It should be clear that this is insufficient to properly match observable discount bond prices, which effectively disqualifies the model from practical pricing applications
Right after that, the book states the following
Fortunately, a remedy is quite straightforward: simply introduce a deterministic function $a(t)$ and alter the model to be $r(t) = r(0) + a(t) + \sigma_rW(t)$ with $a(0) = 0$
- On calibrating this model, how should I go about it? Any particular method that is most popular?
- Why, according to the first quote, can't we fit term structures with Ho-Lee at all? Is this always the case? And specifically how exactly does a time-dependent parameter improve things so much?