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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:

  1. 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 $t$.
  2. 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 $V_{swap}(T_i)$.
  3. 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!

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  • $\begingroup$ What you are doing is comparing the continuation value (entering in the next swaption) versus the exercise value (entering in the current swap). As such, the cash flow you mention is indeed not part of the continuation value (next swaption price) but it should be part of the exercise value (current swap price). $\endgroup$
    – Quantuple
    Oct 4, 2021 at 6:25

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