I've just finished reading through and re-reading through Chapter 14, and have begun to attempt the exercises, and I seem to be completely lost in this chapter. Since I think interest rate derivatives are probably one of the hardest topics in this book, hopefully my questions will be of some use to everyone here.
For one, the displaced diffusion model seems a bit strange to me, and I think it's because I'm not understanding it (in light of exercise 14.1, which I am unable to solve). As you have written in the book, we have:
df = sigma (f+a)dW, where a is some constant.
Question: Is there really no drift in this model?
I ask because in exercise 14.1, it asks for the drift of f (in the measure associated to that particular ZCB), but if the drift is 0 to start with then it seems like this is a non-starter. I've followed through the method you employ in section 14.3, but if I assume that df = sigma (f+a)dW it seems like there's really just nowhere to go (it implies things are 0 that I know shouldn't be).
(Note: As I'm writing this, I do think back to chapter 6, where we didn't make any assumptions on the drift except that it was constant times S(t) and I guess that could include 0....is that still what's going on here also?)