Bermuda Option
A Bermuda option is an options contract that can be exercised on a predetermined set of specific dates before expiration rather than only at expiration (European style) or at any time (American style), sitting between these two extremes in the spectrum of exercise flexibility.
The naming convention reflects geographic positioning between the two main option types: European options (exercisable only at expiration) and American options (exercisable at any time). Bermuda, sitting geographically between Europe and America, gives its name to an option that can be exercised at certain specified intermediate dates — often monthly or quarterly intervals — but not on arbitrary trading days.
Bermuda options are most prevalent in interest rate and fixed income derivatives rather than in equity markets. Bermudan swaptions — options to enter into interest rate swaps that can be exercised on any of the quarterly reset dates of the underlying swap — are among the most actively traded derivatives in the over-the-counter fixed income market. Bond issuers use them to create callable bonds with specific call dates: the issuer has the right to redeem the bond at par on any of several specified future dates rather than at any time.
For equity derivatives, Bermuda options appear in executive compensation plans (where early exercise is permitted at vesting dates), structured products (where the issuer has a call right on certain dates to redeem the note early), and some leveraged finance instruments. CBOE-listed equity options are all American style for the purpose of early exercise, so the Bermuda structure in equity markets exists primarily in the OTC space.
Pricing Bermuda options requires backward-induction methods that account for the optimal early exercise decision at each permitted exercise date. The holder should exercise early if the intrinsic value at a Bermuda exercise date exceeds the continuation value — the expected value of holding the option through further exercise opportunities. Lattice models (binomial and trinomial trees), finite difference methods, and least-squares Monte Carlo are all used for Bermuda option valuation.
The early exercise premium in a Bermuda option is between zero (European) and the American option premium. More exercise dates push the Bermuda option price closer to the American value. For deep-in-the-money options on high-dividend stocks, the Bermuda early exercise feature can be particularly valuable if the exercise dates coincide with ex-dividend periods.