CFA Level II ExamFixed IncomeMedium
A bond portfolio manager uses a binomial interest rate tree to value callable bonds. The tree is calibrated to market yields. When valuing a callable bond, what is the correct approach to determine its value at each node in the tree?
- AThe value at each node is the higher of the call price and the value if not called.
- BThe value at each node is the lower of the put price and the value if not called.
- CThe value at each node is the higher of the put price and the value if not put.
- DThe value at each node is the lower of the call price and the value if not called.
Show answer & explanationAnswer & explanation
Correct answer: D. The value at each node is the lower of the call price and the value if not called.
For a callable bond, the issuer has the right to call the bond. They will exercise this right if the bond's market value (value if not called) exceeds the call price. Therefore, the bondholder will receive no more than the call price. The bond's value at each node is the minimum of the call price and the value if not called.
Why the other options are wrong
- A. Incorrect. The issuer calls the bond, so the bondholder receives the minimum of the call price or the bond's value, not the maximum.
- B. Incorrect. This describes the valuation of a putable bond, not a callable bond.
- C. Incorrect. This describes the valuation of a putable bond, not a callable bond.
Binomial Tree Valuation of Callable Bonds
When valuing a callable bond using a binomial interest rate tree, the bond's value at each node is capped at its call price, reflecting the issuer's option to redeem.
- Start from the final maturity nodes and work backward.
- At each node, calculate the value if not called (discounted expected future values).
- Compare this 'if not called' value with the call price.
- The bond's value is the lower of the two (min(value_if_not_called, call_price)).
Memory trick: Callable bonds are 'capped' by the call price, always 'choosing' the lower value.