The pricing of Bermin Swaptions is complex and there is no analytical formula like Black Shoals.

We can use Bermin have to be priced using numerical approaches such as binomial trees or Monte Carlo models.

The outcome of which depends upon the model chosen and other details such as the calibration methodology used.

As such, the pricing is complex and computationally intense.

However, intuitively we can always use our switching options approach to understand that the value of a Bermuda must always be greater than or equal to the most valuable underlying European swap option, often called the Max European.

The table on screen shows the full price of a five year no call, one year 4% Bermuda receiver versus the price of the individual European swaptions it is composed of.

We can see that the Max European is the first expiry, the one year, four year, and that the Bermin is worth 12 basis points more than this, max European representing the value of the switching options.

The right hand column in the table shows the allocation of that extra 12 basis points as each extra expiry is added.

So if we start with a one year, four year European and add in the possibility to switch to a two year, three year, it adds nine basis points of value.

Adding in the subsequent right to switch to three year, two year, and four year, one year adds a further two and one basis points of value respectively.

Note that the location of the Max European will depend on the volatility surface and the shape of the curve in an upward sloping curve, it's common to see the pattern for Bermuda receivers that we see on the screen with the first expiry being the max European as the forwards make each progressive European less in the money or more out of the money than the one before.