I was reading a technical report by Hagan, which can be downloaded here on the valuation of accrual swaps and range notes.
It caught my attention that in the valuation he comments this:
Consider the $jth$ period of a coupon leg, and suppose the underlying indice is k-month Libor. Let $L(τ_{st})$ be the k-month Libor rate which is fixed for the period starting on date $τ_{st}$ and ending on $τ_{end(τ st)} = τ_{st}+k$ months. The Libor rate will be fixed on a date $τ_{fix}$, which is on or a few days before $τ_{st}$, depending on currency. On this date, the value of the contibution from day $τ_{st}$ is clearly:
\begin{align*} V(τ_{fix},τ_{st})=Z(τ_{fix},t_{j})\Bigg\{\frac{\alpha_jR_{fix}}{M_j} && if &&R_{min} \le L(τ_{st}) \le R_{max} \end{align*}
And $0$ if it's not in the interval.
My confusion here is that he defines and uses three dates in the valuation: fixing date, start date, and end date.
In the prospectus I've used for the valuation of this kind of instruments (range notes in particular) these three dates are stated (fixing date, start coupon date, ending coupon date). But for the valuation, I usually assume that the fixing date equals the start date $t_{fix}=t_{st}$ and discount my payoffs from the ending date. So the start date doesn't play a role in my valuation.
Is it common to have a fixing date prior to the start date and use both dates in the valuation? Would this mean that in each fixing date you use the forward rate that covers the period from the start date to the end date, rather than the actual rate observed on that date?
Much help appreciated