Handling Swap Cash Flows in Bermudan Swaption LSMC

Summary

The document outlines a least-squares Monte Carlo setup for valuing a Bermudan swaption. At the final exercise date, the payoff is the positive part of the underlying swap value. At earlier exercise dates, the method regresses discounted future swaption values on state variables to estimate continuation value, then compares that estimate with immediate exercise value. The question focuses on whether this backward recursion properly accounts for swap payments between exercise dates.

No answer or worked example is supplied, so the document does not resolve the cash-flow treatment. The practical issue it raises is that the continuation target must represent the value of all cash flows belonging to the instrument over the interval, consistently with the chosen valuation convention. Readers should not infer a complete implementation recipe from this prompt alone; they need a model specification that clarifies payment timing, accrued amounts, and how swap value is defined at each exercise date.

Key ideas

• Bermudan swaption LSMC estimates continuation value by regression on simulated state variables.
• At each exercise date, the holder compares continuation value with immediate exercise value.
• The prompt questions whether intermediate swap payments are included in the discounted regression target.
• No response is included, so the document leaves cash-flow handling unresolved.

Tags

# Bermudan Swaption Pricing via Least-Square Monte Carlo


# Bermudan Swaption Pricing via Least-Square Monte Carlo












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!

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