问一道题：NO.PZ201812310200000108 第8小题

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？

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！！！！！！！！！！！！！！！！！

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？

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

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