Baran

 

6、Which of the following is the appropriate "nodal decision" within the backward induction methodology of the interest tree framework for a callable bond?

A) Max(call price, discounted value).

B) Max(par value, discounted value).

C) Min(par value, discounted value).

D) Min(call price, discounted value).

Baran

 

The correct answer is D

When valuing a callable bond using the backward induction methodology, the relevant cash flow to use at each nodal period is the coupon to be received during that nodal period plus the computed value or the call price, whichever is less.

Baran

 

7、A callable bond with an 8.2 percent annual coupon will mature in two years at par value. The current one-year spot rate is 7.9 percent. For the second year, the yield-volatility model forecasts that the one-year rate will be either 6.8 or 7.6 percent. The call price is 101. Using a binomial interest rate tree, what is the current price?

A) 101.140.

B) 100.558.

C) 100.279.

D) 99.759.

Baran

 

The correct answer is A

The tree will have three nodal periods: 0, 1, and 2. The goal is to find the value at node 0. We know the value for all the nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices:

V1,U =[(100+8.2)/1.076+(100+8.2)/1.076]/2 = 100.558

V1,L =[(100+8.2)/1.068+(100+8.2)/1.068]/2= 101.311

Since V1,L is greater than the call price, the call price is entered into the formula below:

V0=[(100.558+8.2)/1.079)+(101.311+8.2)/1.079)]/2 = (100.795 + 101.493) / 2 = 101.14.

Baran

 

8、Suppose that the value of an option-free bond is equal to 100.16, the value of the corresponding callable bond is equal to 99.42, and the value of the corresponding putable bond is 101.72. What is the value of the call option?

A) 0.74.

B) 0.21.

C) 0.64.

D) 1.56.

Baran

 

The correct answer is A

 

The call option value is just the difference between the value of the option-free bond and the value of the callable bond. Therefore, we have:

Call option value = 100.16 – 99.42 = 0.74.

Baran

 

9、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 are adjusted for the bond's convexity to discount the value of the bond.

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

Baran

 

The correct answer is D

 

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.

Baran

 

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

A) The convexity of a bond changes over time.

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

C) Future interest rate changes are difficult to forecast.

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

Baran

 

The correct answer is B

 

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.