开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

kobe42 · 2021年04月11日

如果Discount factore表格没有给,自己怎么算?是求平均的吗?

* 问题详情,请 查看题干

NO.PZ201812310200000108

问题如下:

As previously mentioned, Ibarra is considering a future interest rate volatility of 20% and an upward-sloping yield curve, as shown in Exhibit 2. Based on her analysis, the fair value of bond B2 is closest to:

选项:

A.

€1,101.24.

B.

€1,141.76.

C.

€1,144.63.

解释:

A is correct. The following tree shows the valuation assuming no default of bond B2, which pays a 6% annual coupon.

The scheduled year-end coupon and principal payments are placed to the right of each forward rate in the tree. For example, the Date 4 values are the principal plus the coupon of 60. The following are the four Date 3 values for the bond, shown above the interest rate at each node:

€1,060/1.080804 = €980.75

€1,060/1.054164 = €1,005.54

€1,060/1.036307 = €1,022.86

€1,060/1.024338 = €1,034.81

These are the three Date 2 values:

(0.5×980.75+0.5×1005.54)+60 1.043999 =1008.76

(0.5×1005.54+0.5×1022.86)+60 1.029493 =1043.43

(0.5×1022.86+0.5×1034.81)+60 1.019770 =1067.73

These are the two Date 1 values:

(0.5×1008.76+0.5×1043.43)+60 1.021180 =1063.57

(0.5×1043.43+0.5×1067.73)+60 1.014197 =1099.96

This is the Date 0 value:

(0.5×1063.57+0.5×1099.96)+60 0.997500 =1144.63

So, the value of the bond assuming no default (VND) is 1,144.63. This value could also have been obtained more directly using the benchmark discount factors from Exhibit 2:

€60 × 1.002506 + €60 × 0.985093 + €60 × 0.955848 + €1,060 × 0.913225 = €1,144.63.

The benefit of using the binomial interest rate tree to obtain the VND is that the same tree is used to calculate the expected exposure to default loss. The credit valuation adjustment table is now prepared following these steps:

Step 1: Compute the expected exposures as described in the following, using the binomial interest rate tree prepared earlier.

The expected exposure for Date 4 is €1,060.

The expected exposure for Date 3 is

[(0.1250 × €980.75) + (0.3750 × €1,005.54) + (0.3750 × €1,022.86) + (0.1250 × €1,034.81)] + 60 = €1,072.60.

The expected exposure for Date 2 is

[(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84.

The expected exposure for Date 1 is

[(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76.

Step 2: LGD = Exposure × (1 – Recovery rate)

Step 3: The initial POD, also known as the hazard rate, is provided as 1.50%. For subsequent dates, POD is calculated as the hazard rate multiplied by the previous dates’ POS.

For example, to determine the Date 2 POD (1.4775%), the hazard rate (1.5000%) is multiplied by the Date 1 POS (98.5000%).

Step 4: POS is determined by subtracting the hazard rate from 100% and raising it to the power of the number of years:

(100% – 1.5000%)1 = 98.5000%

(100% – 1.5000%)2 = 97.0225%

(100% – 1.5000%)3 = 95.5672%

(100% – 1.5000%)4 = 94.1337%

Step 5: Expected loss = LGD × POD

Step 6: Discount factors (DF) in Year T are obtained from Exhibit 2.

Step 7: PV of expected loss = Expected loss × DF

Fair value of the bond considering CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24.

如果Discount factore表格没有给,自己怎么算?是求平均的吗?

1 个答案

WallE_品职答疑助手 · 2021年04月11日

嗨,爱思考的PZer你好:


DF其实就是普通的折现,如图

----------------------------------------------
努力的时光都是限量版,加油!

  • 1

    回答
  • 0

    关注
  • 726

    浏览
相关问题

NO.PZ201812310200000108 问题如下 previously mentione Ibarra is consiring a future interest rate volatility of 20% and upwarsloping yielcurve, shown in Exhibit 2. Baseon her analysis, the fair value of bonis closest to: €1,101.24. €1,141.76. €1,144.63. A is correct. The following tree shows the valuation assuming no fault of bonB2, which pays a 6% annucoupon. The scheled year-encoupon anprincippayments are placeto the right of eaforwarrate in the tree. For example, the te 4 values are the principplus the coupon of 60. The following are the four te 3 values for the bon shown above the interest rate each no: €1,060/1.080804 = €980.75 €1,060/1.054164 = €1,005.54 €1,060/1.036307 = €1,022.86 €1,060/1.024338 = €1,034.81 These are the three te 2 values: (0.5�980.75+0.5�1005.54)+60 1.043999 =1008.76 (0.5�1005.54+0.5�1022.86)+60 1.029493 =1043.43 (0.5�1022.86+0.5�1034.81)+60 1.019770 =1067.73 These are the two te 1 values: (0.5�1008.76+0.5�1043.43)+60 1.021180 =1063.57 (0.5�1043.43+0.5�1067.73)+60 1.014197 =1099.96 This is the te 0 value: (0.5�1063.57+0.5�1099.96)+60 0.997500 =1144.63 So, the value of the bonassuming no fault (VN is 1,144.63. This value coulalso have been obtainemore rectly using the benchmark scount factors from Exhibit 2: €60 × 1.002506 + €60 × 0.985093 + €60 × 0.955848 + €1,060 × 0.913225 = €1,144.63. The benefit of using the binomiinterest rate tree to obtain the VNis ththe same tree is useto calculate the expecteexposure to fault loss. The cret valuation austment table is now prepared following these steps: Step 1: Compute the expecteexposures scribein the following, using the binomiinterest rate tree prepareearlier. The expected exposure for te 4 is €1,060. The expected exposure for te 3 is [(0.1250 × €980.75) + (0.3750 × €1,005.54) + (0.3750 × €1,022.86) + (0.1250 × €1,034.81)] + 60 = €1,072.60. The expected exposure for te 2 is [(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84. The expected exposure for te 1 is [(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76. Step 2: LG= Exposure × (1 – Recovery rate) Step 3: The initiPO also known the hazarrate, is provi1.50%. For subsequent tes, POis calculatethe hazarrate multiplied the previous tes’ POS. For example, to termine the te 2 PO(1.4775%), the hazarrate (1.5000%) is multipliethe te 1 POS (98.5000%). Step 4: POS is terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 5: Expecteloss = LG× POD Step 6: scount factors () in YeT are obtainefrom Exhibit 2. Step 7: PV of expecteloss = Expecteloss × Fair value of the bonconsiring CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24. 考试的时候,一般情况下可以用表3图来计算吗?还是必须得用表2先推导出每一个节点的利率?

2023-06-18 22:33 1 · 回答

NO.PZ201812310200000108问题如下 previously mentione Ibarra is consiring a future interest rate volatility of 20% and upwarsloping yielcurve, shown in Exhibit 2. Baseon her analysis, the fair value of bonis closest to: €1,101.24. €1,141.76. €1,144.63. A is correct. The following tree shows the valuation assuming no fault of bonB2, which pays a 6% annucoupon. The scheled year-encoupon anprincippayments are placeto the right of eaforwarrate in the tree. For example, the te 4 values are the principplus the coupon of 60. The following are the four te 3 values for the bon shown above the interest rate each no: €1,060/1.080804 = €980.75 €1,060/1.054164 = €1,005.54 €1,060/1.036307 = €1,022.86 €1,060/1.024338 = €1,034.81 These are the three te 2 values: (0.5�980.75+0.5�1005.54)+60 1.043999 =1008.76 (0.5�1005.54+0.5�1022.86)+60 1.029493 =1043.43 (0.5�1022.86+0.5�1034.81)+60 1.019770 =1067.73 These are the two te 1 values: (0.5�1008.76+0.5�1043.43)+60 1.021180 =1063.57 (0.5�1043.43+0.5�1067.73)+60 1.014197 =1099.96 This is the te 0 value: (0.5�1063.57+0.5�1099.96)+60 0.997500 =1144.63 So, the value of the bonassuming no fault (VN is 1,144.63. This value coulalso have been obtainemore rectly using the benchmark scount factors from Exhibit 2: €60 × 1.002506 + €60 × 0.985093 + €60 × 0.955848 + €1,060 × 0.913225 = €1,144.63. The benefit of using the binomiinterest rate tree to obtain the VNis ththe same tree is useto calculate the expecteexposure to fault loss. The cret valuation austment table is now prepared following these steps: Step 1: Compute the expecteexposures scribein the following, using the binomiinterest rate tree prepareearlier. The expected exposure for te 4 is €1,060. The expected exposure for te 3 is [(0.1250 × €980.75) + (0.3750 × €1,005.54) + (0.3750 × €1,022.86) + (0.1250 × €1,034.81)] + 60 = €1,072.60. The expected exposure for te 2 is [(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84. The expected exposure for te 1 is [(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76. Step 2: LG= Exposure × (1 – Recovery rate) Step 3: The initiPO also known the hazarrate, is provi1.50%. For subsequent tes, POis calculatethe hazarrate multiplied the previous tes’ POS. For example, to termine the te 2 PO(1.4775%), the hazarrate (1.5000%) is multipliethe te 1 POS (98.5000%). Step 4: POS is terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 5: Expecteloss = LG× POD Step 6: scount factors () in YeT are obtainefrom Exhibit 2. Step 7: PV of expecteloss = Expecteloss × Fair value of the bonconsiring CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24. 如题!!!!!!!!!!!!!!!!!

2023-05-17 00:21 1 · 回答

NO.PZ201812310200000108 问题如下 previously mentione Ibarra is consiring a future interest rate volatility of 20% and upwarsloping yielcurve, shown in Exhibit 2. Baseon her analysis, the fair value of bonis closest to: €1,101.24. €1,141.76. €1,144.63. A is correct. The following tree shows the valuation assuming no fault of bonB2, which pays a 6% annucoupon. The scheled year-encoupon anprincippayments are placeto the right of eaforwarrate in the tree. For example, the te 4 values are the principplus the coupon of 60. The following are the four te 3 values for the bon shown above the interest rate each no: €1,060/1.080804 = €980.75 €1,060/1.054164 = €1,005.54 €1,060/1.036307 = €1,022.86 €1,060/1.024338 = €1,034.81 These are the three te 2 values: (0.5�980.75+0.5�1005.54)+60 1.043999 =1008.76 (0.5�1005.54+0.5�1022.86)+60 1.029493 =1043.43 (0.5�1022.86+0.5�1034.81)+60 1.019770 =1067.73 These are the two te 1 values: (0.5�1008.76+0.5�1043.43)+60 1.021180 =1063.57 (0.5�1043.43+0.5�1067.73)+60 1.014197 =1099.96 This is the te 0 value: (0.5�1063.57+0.5�1099.96)+60 0.997500 =1144.63 So, the value of the bonassuming no fault (VN is 1,144.63. This value coulalso have been obtainemore rectly using the benchmark scount factors from Exhibit 2: €60 × 1.002506 + €60 × 0.985093 + €60 × 0.955848 + €1,060 × 0.913225 = €1,144.63. The benefit of using the binomiinterest rate tree to obtain the VNis ththe same tree is useto calculate the expecteexposure to fault loss. The cret valuation austment table is now prepared following these steps: Step 1: Compute the expecteexposures scribein the following, using the binomiinterest rate tree prepareearlier. The expected exposure for te 4 is €1,060. The expected exposure for te 3 is [(0.1250 × €980.75) + (0.3750 × €1,005.54) + (0.3750 × €1,022.86) + (0.1250 × €1,034.81)] + 60 = €1,072.60. The expected exposure for te 2 is [(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84. The expected exposure for te 1 is [(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76. Step 2: LG= Exposure × (1 – Recovery rate) Step 3: The initiPO also known the hazarrate, is provi1.50%. For subsequent tes, POis calculatethe hazarrate multiplied the previous tes’ POS. For example, to termine the te 2 PO(1.4775%), the hazarrate (1.5000%) is multipliethe te 1 POS (98.5000%). Step 4: POS is terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 5: Expecteloss = LG× POD Step 6: scount factors () in YeT are obtainefrom Exhibit 2. Step 7: PV of expecteloss = Expecteloss × Fair value of the bonconsiring CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24. 我老是容易忽略这个要素,导致结果会差一点。这个 是不是就是等于 用无风险利率向前折现的因子?我这么理解对不对?

2023-03-15 11:09 1 · 回答

NO.PZ201812310200000108 问题如下 previously mentione Ibarra is consiring a future interest rate volatility of 20% and upwarsloping yielcurve, shown in Exhibit 2. Baseon her analysis, the fair value of bonis closest to: €1,101.24. €1,141.76. €1,144.63. A is correct. The following tree shows the valuation assuming no fault of bonB2, which pays a 6% annucoupon. The scheled year-encoupon anprincippayments are placeto the right of eaforwarrate in the tree. For example, the te 4 values are the principplus the coupon of 60. The following are the four te 3 values for the bon shown above the interest rate each no: €1,060/1.080804 = €980.75 €1,060/1.054164 = €1,005.54 €1,060/1.036307 = €1,022.86 €1,060/1.024338 = €1,034.81 These are the three te 2 values: (0.5�980.75+0.5�1005.54)+60 1.043999 =1008.76 (0.5�1005.54+0.5�1022.86)+60 1.029493 =1043.43 (0.5�1022.86+0.5�1034.81)+60 1.019770 =1067.73 These are the two te 1 values: (0.5�1008.76+0.5�1043.43)+60 1.021180 =1063.57 (0.5�1043.43+0.5�1067.73)+60 1.014197 =1099.96 This is the te 0 value: (0.5�1063.57+0.5�1099.96)+60 0.997500 =1144.63 So, the value of the bonassuming no fault (VN is 1,144.63. This value coulalso have been obtainemore rectly using the benchmark scount factors from Exhibit 2: €60 × 1.002506 + €60 × 0.985093 + €60 × 0.955848 + €1,060 × 0.913225 = €1,144.63. The benefit of using the binomiinterest rate tree to obtain the VNis ththe same tree is useto calculate the expecteexposure to fault loss. The cret valuation austment table is now prepared following these steps: Step 1: Compute the expecteexposures scribein the following, using the binomiinterest rate tree prepareearlier. The expected exposure for te 4 is €1,060. The expected exposure for te 3 is [(0.1250 × €980.75) + (0.3750 × €1,005.54) + (0.3750 × €1,022.86) + (0.1250 × €1,034.81)] + 60 = €1,072.60. The expected exposure for te 2 is [(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84. The expected exposure for te 1 is [(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76. Step 2: LG= Exposure × (1 – Recovery rate) Step 3: The initiPO also known the hazarrate, is provi1.50%. For subsequent tes, POis calculatethe hazarrate multiplied the previous tes’ POS. For example, to termine the te 2 PO(1.4775%), the hazarrate (1.5000%) is multipliethe te 1 POS (98.5000%). Step 4: POS is terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 5: Expecteloss = LG× POD Step 6: scount factors () in YeT are obtainefrom Exhibit 2. Step 7: PV of expecteloss = Expecteloss × Fair value of the bonconsiring CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24. 如题

2022-08-05 10:56 1 · 回答

NO.PZ201812310200000108问题如下 previously mentione Ibarra is consiring a future interest rate volatility of 20% and upwarsloping yielcurve, shown in Exhibit 2. Baseon her analysis, the fair value of bonis closest to: €1,101.24. €1,141.76. €1,144.63. A is correct. The following tree shows the valuation assuming no fault of bonB2, which pays a 6% annucoupon. The scheled year-encoupon anprincippayments are placeto the right of eaforwarrate in the tree. For example, the te 4 values are the principplus the coupon of 60. The following are the four te 3 values for the bon shown above the interest rate each no: €1,060/1.080804 = €980.75 €1,060/1.054164 = €1,005.54 €1,060/1.036307 = €1,022.86 €1,060/1.024338 = €1,034.81 These are the three te 2 values: (0.5�980.75+0.5�1005.54)+60 1.043999 =1008.76 (0.5�1005.54+0.5�1022.86)+60 1.029493 =1043.43 (0.5�1022.86+0.5�1034.81)+60 1.019770 =1067.73 These are the two te 1 values: (0.5�1008.76+0.5�1043.43)+60 1.021180 =1063.57 (0.5�1043.43+0.5�1067.73)+60 1.014197 =1099.96 This is the te 0 value: (0.5�1063.57+0.5�1099.96)+60 0.997500 =1144.63 So, the value of the bonassuming no fault (VN is 1,144.63. This value coulalso have been obtainemore rectly using the benchmark scount factors from Exhibit 2: €60 × 1.002506 + €60 × 0.985093 + €60 × 0.955848 + €1,060 × 0.913225 = €1,144.63. The benefit of using the binomiinterest rate tree to obtain the VNis ththe same tree is useto calculate the expecteexposure to fault loss. The cret valuation austment table is now prepared following these steps: Step 1: Compute the expecteexposures scribein the following, using the binomiinterest rate tree prepareearlier. The expected exposure for te 4 is €1,060. The expected exposure for te 3 is [(0.1250 × €980.75) + (0.3750 × €1,005.54) + (0.3750 × €1,022.86) + (0.1250 × €1,034.81)] + 60 = €1,072.60. The expected exposure for te 2 is [(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84. The expected exposure for te 1 is [(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76. Step 2: LG= Exposure × (1 – Recovery rate) Step 3: The initiPO also known the hazarrate, is provi1.50%. For subsequent tes, POis calculatethe hazarrate multiplied the previous tes’ POS. For example, to termine the te 2 PO(1.4775%), the hazarrate (1.5000%) is multipliethe te 1 POS (98.5000%). Step 4: POS is terminesubtracting the hazarrate from 100% anraising it to the power of the number of years: (100% – 1.5000%)1 = 98.5000% (100% – 1.5000%)2 = 97.0225% (100% – 1.5000%)3 = 95.5672% (100% – 1.5000%)4 = 94.1337% Step 5: Expecteloss = LG× POD Step 6: scount factors () in YeT are obtainefrom Exhibit 2. Step 7: PV of expecteloss = Expecteloss × Fair value of the bonconsiring CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24. 本题的二叉树构建不是直接根据forwarrate直接求得的,还需要不断调整,这个过程比较复杂,但是后续的计算又在此基础上,这个二叉树构建calibration的过程考试会考吗,我们需要掌握到哪种程度啊

2022-07-31 06:54 1 · 回答