CFA Level II ExamFixed IncomeMedium
An analyst is valuing a bond with an embedded call option using a binomial interest rate tree. The bond has a par value of $1,000, an annual coupon rate of 7%, and a maturity of 3 years. The call price is $1,050. The current 1-year spot rate is 6%. If the bond is callable at the end of Year 1 and Year 2, what would be the first step in the valuation process using the binomial tree?
- ACalculate the intrinsic value of the call option at each node.
- BWork backward from maturity, calculating the bond value at each node at maturity.
- CDetermine the present value of all future cash flows using the current spot rate.
- DEstimate the forward rates and construct the interest rate tree.
Show answer & explanationAnswer & explanation
Correct answer: D. Estimate the forward rates and construct the interest rate tree.
The first step in valuing a bond with embedded options using a binomial interest rate tree is to construct the tree itself. This involves estimating the forward rates for each period and then modeling the possible interest rate paths, ensuring the tree is arbitrage-free.
Why the other options are wrong
- A. Calculating the intrinsic value of the call option is part of the backward induction process, not the first step.
- B. Working backward from maturity is the core of the valuation process, but it occurs after the tree is constructed and populated with rates.
- C. Calculating the present value of cash flows using a single spot rate is for option-free bonds, not typically the first step for a binomial tree valuation of embedded options.
Binomial Tree Valuation (Callable Bond)
Valuing a callable bond using a binomial interest rate tree involves building the tree of possible interest rates and then working backward from maturity, accounting for the issuer's call option.
- Arbitrage-free interest rate tree is essential.
- Backward induction is used.
- At each node, compare callable value to 'stay-alive' value.
Memory trick: Tree first, then backward, checking calls.