When to exercise a physical Bermudan swaption

Question

I have seen a lot of literature regarding the valuation of physical Bermudan Swaptions.

However, I could not find any answer to the following question: if you're a trader and an expiry date is approaching, how do you know if you exercise now or not?

I don't think that it is just by checking if the underlying swap value is bigger than the continuation value (which is the criteria used in valuation models). Here's why with two examples:

Let's imagine you have an expiry frequency of 6 months. I expect the volatility of the remaining Swaptions to almost always compensate for the next coupon except for extreme case.

If the expiry frequency is every 5 years for instance, I cannot believe that a trader would not exercise by strictly applying this criteria without considering the magnitude of the difference between the two figures.

Thanks for your help

Answer 1

You’re generally right. Suppose we have a Bermudian receiver with exercise dates $T_i$ with $\textit{i=1 to (n-1)} $ where $T_n$ is the maturity date of the swap. Then a necessary condition for exercise at $T_1$ would be that all the swap rates $[T_1,T_j]$ are less than the coupon C. Otherwise , you do better by receiving fixed to some date and then exercising later. To determine a sufficient condition for exercise is more difficult and requires a term structure model. When you exercise , you must be sufficiently “in the money” to compensate for all the options you are throwing away. This depends on the volatility structure across the whole yield curve.

(Answering the comment): it’s correct to utilize the general rule : exercise if continuation value < exercise value, which we can write as exercise intrinsic > continuation intrinsic + continuation time value, or $$ Intrinsic[T_1,T_2] > continuationtimevalue $$. Thus indeed if the next period is not deeply through the strike , it is unlikely to overcome the time value being thrown away by exercising.