6．Assume that the bond is putable in one year at par ($100) and that the put will be exercised if the computed value is less than par. What is the value of the putable bond? A) $95.38. B) $105.17. C) $107.56. D) $103.04. The correct answer was B) The relevant value to be discounted using a binomial model and backward induction methodology for a putable bond is the value that will be received if the put option is exercised or the computed value, whichever is greater. In this case, the relevant value at node 1U is the exercise price ($100.000) since it is greater than the computed value of $99.127. At node 1L, the computed value of $103.583 must be used. Therefore, the value of the putable bond is: V0 = (½)[(100.00 + 8) / (1 + 0.043912)] + [(103.583 + 8) / (1 + 0.043912)] = $105.17314
7．Assume that the bond is putable in one year at par ($100) and that the put will be exercised if the computed value is less than par. What is the value of the put option? A) $0.42. B) $1.86. C) $1.08. D) $3.70. The correct answer was A) Vputable = Vnonputable + Vput Rearranging, the value of the put can be stated as: Vput = Vputable − Vnonputable Vputable was computed to be $105.173 in the previous question, and Vnonputable was determined to be $104.755 in the question prior to that. So the value of the embedded put option for the bond under analysis is: $105.173 − 104.755 = $0.418 8．Which of the following statements regarding the option adjusted spread (OAS) is least accurate? A) The OAS is the spread on a bond with an embedded option after the embedded option cost has been removed. B) The OAS for a corporate bond must be calculated using a binomial interest rate model. C) The OAS is equal to the Z-spread plus the option cost. D) Because the binomial interest rate model is created using the spot rate curve, the OAS is also a spread over the spot rate curve. The correct answer was C) The OAS is equal to the Z-spread minus the option cost. All the other choices are true statements. 9．Using the following tree of semiannual interest rates what is the value of a putable bond that has one year remaining to maturity, a put price of 99, coupons paid semiannually with payments based on a 5 percent annual rate of interest? 7.59%
6.35%
5.33% A) 97.92. B) 98.54. C) 98.75. D) 99.00. The correct answer was D) The putable bond price tree is as follows:
| 100.00 | A ==> 99.00 |
| 99.00 |
| 100.00 |
| 99.84 |
| 100.00 | | | |
As an example, the price at node A is obtained as follows: PriceA = max{(prob * (Pup + coupon/2) + prob * (Pdown + coupon/2))/(1 + rate/2), put price} = max{(0.5 * (100 + 2.5) + 0.5 * (100 + 2.5))/(1 + 0.0759/2),99} = 99.00. The bond values at the other nodes are obtained in the same way. The calculated price at node 0 = [.5(99.00+2.5) + .5(99.84+2.5)]/(1+.0635/2) = $98.78 but since the put price is $99 the price of the bond will not go below $99. 10．A putable bond with a 6.4 percent annual coupon will mature in two years at par value. The current one-year spot rate is 7.6 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 bond is putable in one year at 99. Using a binomial interest rate tree, what is the current price? A) 98.190. B) 97.955. C) 98.246. D) 98.885. 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 at all nodes in nodal period 2: V2=100. In nodal period 1, there will be two possible prices: Vi,U =[(100+6.4)/1.076+(100+6.4)/1.076]/2 = 98.885 Vi,L =[(100+6.4)/1.068+(100+6.4)/1.068]/2 = 99.625. Since 98.885 is less than the put price, Vi,U = 99 V0 =[(99+6.4)/1.076)+(99.625+6.4)/1.076)]/2 = 98.246. | 
发表于 2008-4-22 11:26
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