A Bermudan Option is a type of option that can only be exercised on predetermined dates, usually every month. Bermuda options are a combination of American and European style options.
Bermudan options are similar in style to American style options in that there is a possibility of early exercise, but instead of a single exercise date there are predetermined discrete exercise dates. They are commonly used in interest rate and FX markets but we generalise them in this case for any type of options.
The main difficulty in determining suitable valuation for Bermudan options comes in the form of the boundary problem. Because of multiple exercise dates, determining the boundary condition in order to solve the pricing problem can be difficult. By determining the optimal exercise strategy and the respective boundary condition, one can generally use simulation methods to determine suitable prices for Bermudans.
In addition to having predetermined exercise dates, Bermudans also have a ‘early exercise date’ characteristic which we will say is where t = E. This date lies before the predetermined exercise dates, but after t = 0. Between 0 and E, the Bermudan behaves like a European contract and no exercise is possible; and between t = E and t = T, the Bermudan has American style traits. The price of a Bermudan is typically between that of an American option and a European option.
Because a this option has both European and American style properties (but with more American style exercise properties) it was named a Bermudan – in the sense that Bermuda lies between the two regions but closer to the USA.
For example a typical Bermudan swap ion might confer the opportunity to enter into an interest rate swap. The option holder might decide to enter into the swap at the first exercise date (and so enter into, say, a ten-year swap) or defer and have the opportunity to enter in six months time (and so enter a nine-year and six-month swap). Most exotic interest rate options are of Bermudan style.