真题里面考过计算量这么大的题吗？

问题如下：

The wealth management firm has an existing position in bond B4.

B4: A bond similar to B2 but the coupon rate is the one-year benchmark rate plus 4%.

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：

Correct Answer: A

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 (3).

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.