6.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) 100.558.
B) 100.279.
C) 101.000.
D) 99.759.
7.Using the following tree of semiannual interest rates what is the value of a callable bond that has one year remaining to maturity, a call price of 99 and a 5 percent coupon rate that pays semiannually?
7.59%
6.35%
5.33%
A) 98.26.
B) 98.65.
C) 99.21.
D) 99.98.
8.Using the following tree of semiannual interest rates what is the value of a 5 percent callable bond that has one year remaining to maturity, a call price of 99 and pays coupons semiannually?
7.76%
6.20%
5.45%
A) 97.17.
B) 98.29.
C) 99.01.
D) 99.71.
6.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) 100.558.
B) 100.279.
C) 101.000.
D) 99.759.
The correct answer was C)
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+8.2)/1.079)]/2 = 101.000.
7.Using the following tree of semiannual interest rates what is the value of a callable bond that has one year remaining to maturity, a call price of 99 and a 5 percent coupon rate that pays semiannually?
7.59%
6.35%
5.33%
A) 98.26.
B) 98.65.
C) 99.21.
D) 99.98.
The correct answer was A)
The callable bond price tree is as follows:
| 100.00 | |
A ==> 98.75 | | |
98.26 | | 100.00 |
| 99.00 | |
| 100.00 | |
As an example, the price at node A is obtained as follows:
PriceA = min{(prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2), call price} = min{(0.5 * (100 + 2.5) + 0.5 * (100 + 2.5))/(1 + 0.0759/2),99} = 98.75. The bond values at the other nodes are obtained in the same way.
8.Using the following tree of semiannual interest rates what is the value of a 5 percent callable bond that has one year remaining to maturity, a call price of 99 and pays coupons semiannually?
7.76%
6.20%
5.45%
A) 97.17.
B) 98.29.
C) 99.01.
D) 99.71.
The correct answer was B)
The callable bond price tree is as follows:
| 100.00 | |
A ==> 98.67 | | |
98.29 | | 100.00 |
| 99.00 | |
| 100.00 | |
As an example, the price at node A is obtained as follows:
PriceA = min{(prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2), call price} = min{(0.5 * (100 + 2.5) + 0.5 * (100 + 2.5))/(1 + 0.0776/2),99} = 98.67. The bond values at the other nodes are obtained in the same way.
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