spartan1

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 are weighted by the bond's duration to discount the value of the bond.

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

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

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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.

spartan1

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.

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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."

spartan1

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

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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 e2 × σ. Neither of the other sets of information are sufficient for constructing the tree.

spartan1

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

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

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

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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.