Learn / Risk & ALM
Bermudan exercise
A Bermudan swaption can be exercised on more than one date. On each date the holder compares the value of entering the swap now with the value of keeping the option.
01
Exercise now, or wait
Exercise value is the payoff of entering the swap on that date. Continuation value is what the remaining option is worth if the holder waits. The holder exercises only when the exercise value is greater. On the last date there is no remaining option, so continuation is zero: exercise, or let it expire.
Walk the lab’s starting rate of 4.2% with the strike at 4%, notional $100 million, and annuity 8. The rate gap is 0.20 percentage points, so the exercise value is $100 million × 8 × 0.002 = $1.6 million on every date. Year 1 continuation is $2.5 million, and $1.6 million is smaller, so the holder waits. Year 3 continuation is $0.9 million, and $1.6 million is larger, so exercise wins. Year 5 continuation is $0, so the last date is exercise or expire.
Teaching lab
Exercise or wait
Continuation values are labeled classroom hurdles, not the output of a tree. Exercise when the exercise value is greater. Year 5 is the last date, so waiting is worth zero.
| Date | Exercise | Continuation | Choice |
|---|---|---|---|
| Year 1 | $1,600,000 | $2,500,000 | Wait |
| Year 3 | $1,600,000 | $900,000 | Exercise |
| Year 5 | $1,600,000 | $0 | Exercise |
02
What a book actually runs
A European price is one exercise date, so there is no earlier choice. A Bermudan price has to know the value of waiting on every earlier date. A real book replaces the continuation column with a tree or with regression Monte Carlo. This lab does not run that solver. The continuation numbers are labeled hurdles so the comparison is visible. Move the rate and the exercise column changes. The hurdles stay put.
The short-rate path that would feed those dates is the Hull–White lesson.