Bermin swaptions are options with multiple discreet expiry dates.

So the option can be exercised once, but on a choice of different predetermined expiry dates.

Bermin options only rarely exist in the interest rate world where their expiry dates can be matched against the payment dates of bonds or swaps to create callable and putable structures.

As can be seen on screen, ber mutants are traded on co terminal underlying swaps, which means that the option is exercised into a swap, which always has the same final maturity date.

For example, imagine we have a five year no call, one year annual exercise bermin.

This is an option that can be exercised in year 1, 2, 3, or four into a swap, which had a five year maturity date when seen from the trade date.

So if the option is exercised in one year, it is into a four year swap.

However, if that exercise opportunity is passed up and instead the option is exercised in two years, it is into a three year swap.

Hence, as the exercise gets longer, the underlying swap gets shorter.

One useful way of thinking about Bermudans is to consider them to be a European style swap option with an expiry equal to the nearest expiry date, and then a set of switching options to switch the expiry date to a later one.

So in the case of our five year, no call one year, this formulation would say the bermin is a one year, four year European swap with the option to switch to a two year, three year European, and then to a three year, two year European and so on.

The slide refers to these as contingent Europeans.

This thought process also helps us to understand that bermudan will usually have a price which is higher than the most valuable of the possible European swaptions because the switching options will usually have some positive value.

In the event that the switching options are worth nothing, then the bermin price will be equal to that of the most valuable European swap.