NO.PZ201812310200000111
问题如下：
The wealth management firm has an existing position in bond B4. The market price of B4, a floating-rate note, is €1,070. Senior management has asked Ibarra to make a recommendation regarding the existing position. Based on the assumptions used to calculate the estimated fair value only, her recommendation should be to:
选项：
A.add to the existing position.
B.hold the existing position.
C.reduce the existing position.
解释：
A is correct. The following tree shows the valuation assuming no default of floating-rate note (FRN) B4, which has a quoted margin of 4%.
The scheduled year-end coupon and principal payments are placed to the right of each forward rate in the tree. For example, the four Date 4 values are the principal plus the coupon.
€1,000 × (1 + 0.080804 + 0.04) = €1,120.80
€1,000 × (1 + 0.054164 + 0.04) = €1,094.16
€1,000 × (1 + 0.036307 + 0.04) = €1,076.31
€1,000 × (1 + 0.024338 + 0.04) = €1,064.34
The following are the four Date 3 bond values for the note, shown above the interest rate at each node:
€1,120.80/1.080804 = €1,037.01
€1,094.16/1.054164 = €1,037.94
€1,076.31/1.036307 = €1,038.60
€1,064.34/1.024338 = €1,039.05
The three Date 3 coupon amounts are computed based on the interest rate at Date 2 plus the quoted margin of 4%:
€1,000 × (0.043999 + 0.04) = €84.00
€1,000 × (0.029493 + 0.04) = €69.49
€1,000 × (0.019770 + 0.04) = €59.77
There are three Date 2 bond values:
The two Date 2 coupon amounts are computed based on the interest rate at Date 1 plus the quoted margin of 4%:
€1,000 × (0.021180 + 0.04) = €61.18
€1,000 × (0.014197 + 0.04) = €54.20
The Date 1 coupon amount is computed based on the interest rate at Date 0 plus the quoted margin of 4%:
€1,000 × (–0.0025 + 0.04) = €37.50
These are the calculations for the bond values for Date 1 and Date 0:
Then, the VND is calculated as follows:
The expected exposures are then computed using the binomial interest rate tree prepared earlier.
For example, the expected exposure for Date 4 is computed as follows:
[(0.125 × €1,120.80) + (0.375 × €1,094.16) + (0.375 × €1,076.31) + (0.125 × €1,064.34)] = €1,087.07
Similarly, the expected exposure for Date 3 is computed as follows:
[(0.125 × €1,037.01) + (0.375 × €1,037.94) + (0.375 × €1,038.60) + (0.125 × €1,039.05)] + [(0.250 × €84) + (0.500 × €69.49) + (0.250 × €59.77)] = €1,108.90
The expected exposures for Dates 2 and 1 are computed similarly, and the credit valuation adjustment table is completed following Steps 2–7 outlined in the solution to Question 8.
Fair value of the FRN considering CVA = €1,154.27 – CVA = €1,154.27 – €44.43 = €1,109.84.
Because the market price of €1,070 is less than the estimated fair value, the analyst should recommend adding to existing positions in the FRN.
B and C are incorrect because the FRN is perceived to be undervalued in the market.
我没有用二叉树，用的是exhibit 2中forward rate。coupon就是forward rate+4%,从date 4一期一期向前折现求exposure。也能得到Fair value为1109.839
但是计算大大简化了。如果考试有forward rate，可以用吗？
