I have some confusion regarding pricing a Bermudan Swaption using LSMC.
Let's say the underlying swap has payment dates $T_0 < T_1 < \ldots < T_n$ and for simplicity, assuming the exercise dates are $T_1 < \ldots < T_{n-1}$. Here is the pricing mechanism that I have found from some reference:
- At the last exercise date $T_{n-1}$, the value of the swaption is $V(T_{n-1}) = \max(V_{swap}(T_{n-1}), 0)$ where $V_{swap}(t)$ is the underlying swap value at time $t$.
- Rolling back from $T_{i+1}$ to $T_i$, the continuation value $C(T_i)$ is estimated by regressing state variables on the the discounted swaption value $\frac{B(T_{i})}{B(T_{i+1})}V(T_{i+1})$, where $B(t)$ is the risk-neutral numeraire. And the exercise value is just the underlying swap value $V_{swap}(T_i)$.
- The value is chosen as the maximum between the continuation value and the exercise value: $$V(T_i) = \max(C(T_i), V_{swap}(T_i))$$
My question is, while implementing above process, how should we take the cash flow of the underlying swap into consideration? From my understanding, the continuation value $C(T_i)$ which is estimated from future swaption value $V(T_{i+1})$ does not consider the cash flow of the payment period $[T_i, T_{i+1}]$?
Thank you very much!
