Reading 57: LOS c ～ Q1- 5

1.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 an MBS only depend on the current rate, not the path that rates have followed.

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

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

D)   interest rates are irrelevant to the value of a mortgage-backed security.

The correct answer was B)

A binomial model or any other model that uses the backward induction method cannot be used to value an MBS because the cash flows for the MBS are dependent upon the path that interest rates have followed.

2.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)   beginning interest rate at the root only.

B)   lowest interest rate in each nodal period.

C)   beginning price of the bond at the root.

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

The correct answer was B)

Given the lowest interest rate in each nodal period, the interest rates at the other nodes can be calculated. The interest rate at any node above the lowest is larger than the one below it by a factor of e^2*σ. None of the other sets of information is sufficient for constructing the tree.

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

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

B)   convexity from duration.

C)   duration from convexity.

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

The correct answer was A)

Backward induction refers to the process of valuing a bond using a binomial interest rate tree. For a bond that has N compounding periods, the current value of the bond is determined by computing the bond’s possible values at period N and working "backwards."

4.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)   The convexity of a bond changes over time.

C)   Future interest rate changes are difficult to forecast.

D)   The mathematical properties of a forward difference scheme are not tractable.

The correct answer was A)

The objective is to value a bond's current price while the bond price at maturity is known. Therefore, price at maturity is used as a starting point, and we work backward to the current value.

5.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)   a deterministic interest rate path is 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)   the corresponding interest rates and interest rate probabilities are used to discount the value of the bond.

D)   the corresponding interest rates are adjusted for the bond's convexity to discount the value of the bond.

The correct answer was C)

For a bond that has N compounding periods, the current value of the bond is determined by computing the bond’s possible values at period N and working “backwards” to the present. The value at any given node is the probability-weighted average of the discounted values of the next period’s nodal values.