Reading 55: Valuing Bonds with Embedded Options-LOS c~Q1-10

backward, valuation, following, framework

LOS c: Illustrate the backward induction valuation methodology within the binomial interest rate tree framework.

Q1. Using the following interest rate tree of semiannual interest rates what is the value of an option free bond that has one year remaining to maturity and has a 5% semiannual coupon rate?

7.30%

6.20%

5.90%

A) 98.98.

B) 98.67.

C) 97.53.

Q2. Using the following interest rate tree of semiannual interest rates what is the value of an option free semiannual bond that has one year remaining to maturity and has a 6% coupon rate?

6.53%
6.30%
5.67%

A) 99.81.

B) 98.52.

C) 97.53.

Q3. For a putable bond, callable bond, or putable/callable bond, the nodal-decision process within the backward induction methodology of the interest rate tree framework requires that at each node the possible values will:

A) include the face value of the bond.

B) not be higher than the call price or lower than the put price.

C) be, in number, two plus the number of embedded options.

Q4. A bond with a 10% annual coupon will mature in two years at par value. The current one-year spot rate is 8.5%. For the second year, the yield volatility model forecasts that the one-year rate will be either 8% or 9%. Using a binomial interest rate tree, what is the current price?

A) 101.837.

B) 103.572.

C) 102.659.

Q5. A bond with a 12% annual coupon will mature in two years at par value. The current one-year spot rate is 14%. For the second year, the yield volatility model forecasts a lower bound of 12% for the one-year rate and a standard deviation of 10%. In a binomial interest rate tree describing this situation, what are the forecasted values for the bond in the first nodal period?

V_1,U: upper rate value V_1,L: lower rate value

A) 97.683 100.000

B) 97.680 101.125

C) 94.676 97.664

Q6. Which of the following is a correct statement concerning the backward induction technique used within the binomial interest rate tree framework? From the maturity date of a bond:

A) the corresponding interest rates and interest rate probabilities are used to discount the value of the bond.

B) the corresponding interest rates are weighted by the bond's duration to discount the value of the bond.

C) a deterministic interest rate path is used to discount the value of the bond.

Q7. Why is the backward induction methodology used to value a bond rather than a forward induction scheme?

A) The price of the bond is known at maturity.

B) Future interest rate changes are difficult to forecast.

C) The convexity of a bond changes over time.

Q8. With respect to interest rate models, backward induction refers to determining:

A) convexity from duration.

B) one portion of the yield curve from another portion.

C) the current value of a bond based on possible final values of the bond.

Q9. For an option-free bond where the coupons and maturity value are known and assuming constant interest rate volatility, which of the following sets of information will allow an analyst to construct the entire tree? The:

A) lowest interest rate in each nodal period.

B) beginning interest rate at the root only.

C) interest rate at the root and in the final nodal period.

Q10. A binomial model or any other model that uses the backward induction method cannot be used to value a mortgage-backed security (MBS) because:

A) the cash flows for the MBS are dependent upon the path that interest rates follow.

B) the prepayments occur linearly over the life of an interest rate trend (either up or down).

C) the cash flows for an MBS only depend on the current rate, not the path that rates have followed.