A portfolio manager is using a binomial interest rate tree to value a 5-year, 5% annual coupon callable bond. The call option allows the issuer to call the bond at par starting from the end of year 2. After constructing the tree and working backward, the manager arrives at the value of the bond at a specific node in year 2 as $1,020, before considering the call option. The call price at that node is $1,000. What is the value of the callable bond at this node?
- A$1,010
- B$1,000
- C$1,020
- D$980
Show answer & explanationAnswer & explanation
Correct answer: B. $1,000
When valuing a callable bond using a binomial tree, at each node where the bond is callable, the value of the callable bond is the minimum of its straight (option-free) value and the call price. This is because the issuer will exercise the call option if the bond's market value exceeds the call price, effectively capping the bond's value at the call price. In this case, the straight value is $1,020 and the call price is $1,000, so the callable bond's value is $1,000.
Why the other options are wrong
- A. This value is arbitrary and does not follow the valuation rule for callable bonds.
- C. This would be the value if the bond were not callable, or if the call price was higher than $1,020.
- D. This would imply the bond's value is below the call price, which is incorrect if the straight value is higher.
Binomial Tree Valuation of Callable Bonds
When valuing a callable bond using a binomial interest rate tree, at any node where the bond is callable, its value is determined as the minimum of the calculated value of the comparable option-free bond and the specified call price. This reflects the issuer's right to call the bond if its market value exceeds the call price.
- Work backward from maturity to the present.
- At each node, calculate the expected future value discounted at the forward rate.
- If the bond is callable at a node, the value is min(straight bond value, call price).
- If the bond is putable, the value is max(straight bond value, put price).
Memory trick: Callable bonds are 'Capped' by the Call Price.