Black-Karasinski - Model Parameters

[tibbar]

I'm looking at the Black-Karasinski class and had a couple of questions about the parameterisation.

It seems that theta(t) is being used to exactly fit the initial term structure? (as described in Brigo & Mercurio).

If so, is it possible to use it in the more simple way, where we instead specify r(0) and theta as a constant parameter?

i.e. the model becomes:

d ln r_t = (theta - alpha d ln r_t) dt + sigma dW_t

and r(0) is used in the tree method to calculate the term structure.