6.A bond with a 12 percent annual coupon will mature in two years at par value. The current one-year spot rate is 14 percent. For the second year, the yield volatility model forecasts a lower bound of 12 percent for the one-year rate and a standard deviation of 10 percent. In a binomial interest rate tree describing this situation, what are the forecasted values for the bond in the first nodal period? A) V1,U: upper rate value = 97.683; V1,L: lower rate value = 100.000. B) V1,U: upper rate value = 94.676; V1,L: lower rate value = 97.664. C) V1,U: upper rate value = 101.125; V1,L: lower rate value = 100.000. D) V1,U: upper rate value = 97.680; V1,L: lower rate value = 101.125. The correct answer was A) The value of the bond for the lower rate is easy; since that forecasted rate is the coupon rate: V1,L=100. The value for the upper rate will be determined by the lower rate and the standard deviation: i1,U=i1,L*(e2*s)=0.12*(e0.20)=0.14657. Thus, V1,U =112/1.14657=97.683. 7.A bond with a 10 percent annual coupon will mature in two years at par value. The current one-year spot rate is 8.5 percent. For the second year, the yield volatility model forecasts that the one-year rate will be either eight or nine percent. Using a binomial interest rate tree, what is the current price? A) 103.572. B) 101.837. C) 101.761. D) 102.659. The correct answer was D) 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 in nodal period 2: V2=100. In nodal period 1, there will be two possible prices: V1,U=[(100+10)/1.09+(100+10)/1.09]/2= 100.917 V1,L=[(100+10)/1.08+(100+10)/1.08]/2= 101.852 Thus V0=[(100.917+10)/1.085+(101.852+10)/1.085]/2= 102.659 8.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) be, in number, two plus the number of embedded options. C) be, in number, two times the number of embedded options. D) not be higher than the call price or lower than the put price. The correct answer was D) At each node, there will only be two values. At each node, the analyst must determine if the initially calculated values will be below the put price or above the call price. If a calculated value falls below the put price: Vi,U=the put price. Likewise, if a calculated value falls above the call price, then Vi,L =the call price. Thus the put and call price are lower and upper limits, respectively, of the bond’s value at a node. 9.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 percent coupon rate? 6.53%
6.30%
5.67% A) 97.53. B) 98.52. C) 100.16. D) 99.81. The correct answer was D) The option-free bond price tree is as follows:
| 100.00 | A ==> 99.74 |
| 99.81 |
| 100.00 |
| 100.16 |
| 100.00 | | | |
As an example, the price at node A is obtained as follows: PriceA = (prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2) = (0.5 * (100 + 3) + 0.5 * (100 + 3))/(1 + 0.0653/2) = 99.74. The bond values at the other nodes are obtained in the same way. The calculation for node 0 or time 0 is 0.5[(99.74 + 3)/(1+ .063/2) + (100.16 + 3)/(1 + .063/2)] = 0.5 (99.60252 + 100.00969) = 99.80611 10.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 percent semiannual coupon rate? 7.30%
6.20%
5.90% A) 97.53. B) 98.98. C) 99.71. D) 98.67. The correct answer was D) The option-free bond price tree is as follows:
| 100.00 | A ==> 98.89 |
| 98.67 |
| 100.00 |
| 99.56 |
| 100.00 | | | |
As an example, the price at node A is obtained as follows: PriceA = (prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2) = (0.5 * (100 + 2.5) + 0.5 * (100 + 2.5))/(1 + 0.0730/2) = 98.89. The bond values at the other nodes are obtained in the same way. The calculation for node 0 or time 0 is 0.5[(98.89 + 2.5)/(1+ .062/2) + (99.56 + 2.5)/(1 + .062/2)] = 0.5 (98.3414 + 98.9913) = 98.6663 | 
发表于 2008-4-22 10:23
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