When pricing a bond via a short rate model on a tree, it seems natural to include intermediate time steps in addition to those corresponding to cashflow dates (i.e. for bonds with American style embedded options).
One thing which isn't clear to me is how to handle the case of floating coupons when there are multiple time steps between an IBOR fixing date and a cashflow date. In particular which IBOR fixing should be assumed to drive the cashflows at the pay date nodes?
It seems like the correct approach would be to:
start with a tree composed of nodes indexed by time and rate - node[t_i, r_j], say
take for example two times t0, t1 where t0 corresponds to a fixing date and t1 a payment date and assume there exist some intermediate time steps between t0 and t1 on the tree
compute the expected value at each node[t0, r_j] by averaging/discounting back across all node[t1, r_k] such that the transition probability (t0, r_j)->(t1, r_k) is non-zero, using the fixing rate determined at node[t0, r_j] to project cashflows at all node[t1, r_k]
Is my intuition on this approach correct? All of the reference implementations I have found simply assume that all node time steps fall exactly on cashflow dates an so this implementation detail is not quite explicitly handled.
Any insights/references would be much appreciated.