A callable bond and an option-free bond can carry the same coupon, maturity, and issuer, yet respond to a 100 bp rate drop in completely different ways. The difference is an option you never see quoted separately.
An embedded option is a contingency provision written into the bond's indenture. It cannot be stripped out and traded on its own. Corresponding to every embedded option is an underlying option-free bond, called the straight bond, with a specified issuer, maturity, principal, coupon, and currency.
- Call option: an issuer right to redeem early, exercised when rates fall or the issuer's credit improves.
- Put option: an investor right to sell the bond back, usually at par, exercised when rates rise. Puts are European or rarely Bermudan; American-style puts do not exist.
- Extension option: the holder may keep the bond outstanding past maturity, possibly at a different coupon.
- Conversion option: the holder may convert into the issuer's common stock.
- Estate put: the heirs may put the bond at par on the holder's death, so value depends on life expectancy.
Common mistakes
- Adding the call value instead of subtracting. The investor is short the call. Using 102.114 + 0.574 = 102.688 instead of 101.540 is the standard distractor.
- Discounting the reset value with the wrong rate. After resetting a node to the exercise price, that reset value feeds the parent node's expectation. Using the original 100.526 rather than 100.000 in Example 1's down node inflates the price.
- Assuming a higher OAS always means cheap. OAS is only comparable at the same volatility assumption. A callable bond's OAS shrinks purely from raising assumed volatility, with no change in credit.
Bottom line
- Callable value: straight bond minus call value. Putable value: straight bond plus put value
- Volatility up: both option values up, callable price down, putable price up
- Rates down: call value up and callable upside capped. Rates up: put value up and putable downside cushioned
- Curve flattening or inversion raises call value and lowers put value
Exam shortcut
On a tree question, write the exercise rule on the page before you compute: issuer calls when node value exceeds the call price, investor puts when node value falls below the put price. Reset first, then discount, and always average the two successors at 0.5 before adding the coupon.
The full lesson (about 3,024 words, 20 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- embedded options
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