问一道题：NO.PZ2019011002000009 [ CFA II ]

NO.PZ2019011002000009问题如下BonC is a 4-yecorporate bon The bonis a floating rate bonanits coupon rate is the one-yebenchmark rate plus 4%. Assume the risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50%, anthe recovery rate is 25%.The current spot rates anforwarrates are shown in the table below:Li, a cret analyst in a wealth management firm, believes ththe future interest rate volatility is 20%.He constructea binomiinterest rate tree using his volatility estimation anthe current yielcurve.The binomiinterest rate tree is shown below:The market priof this floating rate bonis 1054 currently. Accorng to the information above, comparewith the bons fair value, the value of the bonis:A.Unrvalue.Overvalue.Fairly-valueA is correct.考点使用二叉树对有风险的浮动利率债券进行估值解析本题是要计算Floating-rate bonFair value；首先需要用二叉树模型计算其VN有该浮动利率债券的Coupon为Benchmark rate加上4%，因此te 4的Coupon rate出现的情况有8.0804%+4%；5.4164%+4%；3.6307%+4%；2.4338%+4%因此te 4现金流的情况1000×(1+0.080804+0.04)=1120.801000×(1+0.054164+0.04)=1094.161000×(1+0.036307+0.04)=1076.311000×(1+0.024338+0.04)=1064.34由te 4的现金流和二叉树所示利率，可以折现求得te 3四个节点的Value:1120.80/1.080804=1037.011094.16/1.054164=1037.941076.31/1.036307=1038.601064.34/1.024338=1039.05由te 2的Benchmark利率可以知道在te 3三个节点Coupon rate出现的情况有4.3999%+4%；2.9493%+4%；1.9770%+4%因此te 3 Coupon现金流的情况1000×（0.043999+0.04）=841000×（0.029493+0.04）=69.491000×（0.019770+0.04）=59.77将te 3各个节点的Coupon加上te 3各个节点的Value构成te 3的总现金流，利用二叉树向te 2折现[(0.5×1037.01+0.5×1037.94)+84]/1.043999=1074.21[(0.5×1037.94+0.5×1038.60)+69.49]/1.029493=1076.03[(0.5×1038.60+0.5×1039.05)+59.77]/1.019770=1077.30te 2的两个节点的Coupon由te 1 Benchmark利率决定，因此te 1的Coupon rate出现的情况有2.1180%+4%；1.4197%+4%；因此te 2 coupon现金流的情况1000×（0.021180+0.04）= 61.181000×（0.014197+0.04）= 54.20te 2的Coupon现金流加上Value现金流构成te 2的总现金流向te 1折现(1074.21×0.5+1076.03×0.5+61.18)/(1+2.1180%)=1112.73(1076.03×0.5+1077.30×0.5+54.20)/(1+1.4197%)=1115.03te 1的Coupon由te 0时刻Benchmark利率决定，因此te 1的Coupon rate有-0.25%+4%则te 1的Coupon为1000×（-0.0025+0.04）= 37.50te 1的Coupon现金流加上Value现金流构成te 1的总现金流向te0折现(1112.73×0.5+1115.03×0.5+37.50)/(1-0.25%)=1154.27这个1154.27为债券的VN下面利用二叉树计算债券的CVA；te 4的Exposure为0.125×1120.80+0.375×1094.16+0.375×1076.31+0.125×1064.34=1087.07te 3的Exposure为0.125×1037.01+0.375×1037.94+0.375×1038.60+0.125×1039.05+0.250×84+0.5×69.49+0.250×59.77=1108.90te 2的Exposure为0.25×1074.21+0.5×1076.03+0.25×1077.30+61.18×0.5+54.20×0.5=1133.583te 1的Exposure为1112.73×0.5+1115.03×0.5+37.50=1151.38由以上Exposure数据，已知Recovery rate为25%，所以可以知道Recovery；再用Exposure减去Recovery可以得到Loss given fault (LG；本题 hazarrate为1.5%，则可以算出POS以及对应PO再用违约损失LG以违约概率PO到预期损失Expecteloss；Expecteloss通过折现因子求得PV(EL)；加总即得到债券的CVA；因此由债券的VN去其CVA可以的到Fair value1154.27 – 47.6019 = 1106.67；已知当前债券的市场价格为1054；则可以改债券是相对被低估的。(1112.73×0.5+1115.03×0.5+37.50)/(1-0.25%)=1154.27 这个1154.27为债券的VN这个算出来是1535.17啊，是算错了吗

NO.PZ2019011002000009 问题如下 BonC is a 4-yecorporate bon The bonis a floating rate bonanits coupon rate is the one-yebenchmark rate plus 4%. Assume the risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50%, anthe recovery rate is 25%.The current spot rates anforwarrates are shown in the table below:Li, a cret analyst in a wealth management firm, believes ththe future interest rate volatility is 20%.He constructea binomiinterest rate tree using his volatility estimation anthe current yielcurve.The binomiinterest rate tree is shown below:The market priof this floating rate bonis 1054 currently. Accorng to the information above, comparewith the bons fair value, the value of the bonis: A.Unrvalue B.Overvalue C.Fairly-value A is correct.考点使用二叉树对有风险的浮动利率债券进行估值解析本题是要计算Floating-rate bonFair value；首先需要用二叉树模型计算其VN有该浮动利率债券的Coupon为Benchmark rate加上4%，因此te 4的Coupon rate出现的情况有8.0804%+4%；5.4164%+4%；3.6307%+4%；2.4338%+4%因此te 4现金流的情况1000×(1+0.080804+0.04)=1120.801000×(1+0.054164+0.04)=1094.161000×(1+0.036307+0.04)=1076.311000×(1+0.024338+0.04)=1064.34由te 4的现金流和二叉树所示利率，可以折现求得te 3四个节点的Value:1120.80/1.080804=1037.011094.16/1.054164=1037.941076.31/1.036307=1038.601064.34/1.024338=1039.05由te 2的Benchmark利率可以知道在te 3三个节点Coupon rate出现的情况有4.3999%+4%；2.9493%+4%；1.9770%+4%因此te 3 Coupon现金流的情况1000×（0.043999+0.04）=841000×（0.029493+0.04）=69.491000×（0.019770+0.04）=59.77将te 3各个节点的Coupon加上te 3各个节点的Value构成te 3的总现金流，利用二叉树向te 2折现[(0.5×1037.01+0.5×1037.94)+84]/1.043999=1074.21[(0.5×1037.94+0.5×1038.60)+69.49]/1.029493=1076.03[(0.5×1038.60+0.5×1039.05)+59.77]/1.019770=1077.30te 2的两个节点的Coupon由te 1 Benchmark利率决定，因此te 1的Coupon rate出现的情况有2.1180%+4%；1.4197%+4%；因此te 2 coupon现金流的情况1000×（0.021180+0.04）= 61.181000×（0.014197+0.04）= 54.20te 2的Coupon现金流加上Value现金流构成te 2的总现金流向te 1折现(1074.21×0.5+1076.03×0.5+61.18)/(1+2.1180%)=1112.73(1076.03×0.5+1077.30×0.5+54.20)/(1+1.4197%)=1115.03te 1的Coupon由te 0时刻Benchmark利率决定，因此te 1的Coupon rate有-0.25%+4%则te 1的Coupon为1000×（-0.0025+0.04）= 37.50te 1的Coupon现金流加上Value现金流构成te 1的总现金流向te0折现(1112.73×0.5+1115.03×0.5+37.50)/(1-0.25%)=1154.27这个1154.27为债券的VN下面利用二叉树计算债券的CVA；te 4的Exposure为0.125×1120.80+0.375×1094.16+0.375×1076.31+0.125×1064.34=1087.07te 3的Exposure为0.125×1037.01+0.375×1037.94+0.375×1038.60+0.125×1039.05+0.250×84+0.5×69.49+0.250×59.77=1108.90te 2的Exposure为0.25×1074.21+0.5×1076.03+0.25×1077.30+61.18×0.5+54.20×0.5=1133.583te 1的Exposure为1112.73×0.5+1115.03×0.5+37.50=1151.38由以上Exposure数据，已知Recovery rate为25%，所以可以知道Recovery；再用Exposure减去Recovery可以得到Loss given fault (LG；本题 hazarrate为1.5%，则可以算出POS以及对应PO再用违约损失LG以违约概率PO到预期损失Expecteloss；Expecteloss通过折现因子求得PV(EL)；加总即得到债券的CVA；因此由债券的VN去其CVA可以的到Fair value1154.27 – 47.6019 = 1106.67；已知当前债券的市场价格为1054；则可以改债券是相对被低估的。 谢谢！

NO.PZ2019011002000009问题如下BonC is a 4-yecorporate bon The bonis a floating rate bonanits coupon rate is the one-yebenchmark rate plus 4%. Assume the risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50%, anthe recovery rate is 25%.The current spot rates anforwarrates are shown in the table below:Li, a cret analyst in a wealth management firm, believes ththe future interest rate volatility is 20%.He constructea binomiinterest rate tree using his volatility estimation anthe current yielcurve.The binomiinterest rate tree is shown below:The market priof this floating rate bonis 1054 currently. Accorng to the information above, comparewith the bons fair value, the value of the bonis:A.Unrvalue.Overvalue.Fairly-valueA is correct.考点使用二叉树对有风险的浮动利率债券进行估值解析本题是要计算Floating-rate bonFair value；首先需要用二叉树模型计算其VN有该浮动利率债券的Coupon为Benchmark rate加上4%，因此te 4的Coupon rate出现的情况有8.0804%+4%；5.4164%+4%；3.6307%+4%；2.4338%+4%因此te 4现金流的情况1000×(1+0.080804+0.04)=1120.801000×(1+0.054164+0.04)=1094.161000×(1+0.036307+0.04)=1076.311000×(1+0.024338+0.04)=1064.34由te 4的现金流和二叉树所示利率，可以折现求得te 3四个节点的Value:1120.80/1.080804=1037.011094.16/1.054164=1037.941076.31/1.036307=1038.601064.34/1.024338=1039.05由te 2的Benchmark利率可以知道在te 3三个节点Coupon rate出现的情况有4.3999%+4%；2.9493%+4%；1.9770%+4%因此te 3 Coupon现金流的情况1000×（0.043999+0.04）=841000×（0.029493+0.04）=69.491000×（0.019770+0.04）=59.77将te 3各个节点的Coupon加上te 3各个节点的Value构成te 3的总现金流，利用二叉树向te 2折现[(0.5×1037.01+0.5×1037.94)+84]/1.043999=1074.21[(0.5×1037.94+0.5×1038.60)+69.49]/1.029493=1076.03[(0.5×1038.60+0.5×1039.05)+59.77]/1.019770=1077.30te 2的两个节点的Coupon由te 1 Benchmark利率决定，因此te 1的Coupon rate出现的情况有2.1180%+4%；1.4197%+4%；因此te 2 coupon现金流的情况1000×（0.021180+0.04）= 61.181000×（0.014197+0.04）= 54.20te 2的Coupon现金流加上Value现金流构成te 2的总现金流向te 1折现(1074.21×0.5+1076.03×0.5+61.18)/(1+2.1180%)=1112.73(1076.03×0.5+1077.30×0.5+54.20)/(1+1.4197%)=1115.03te 1的Coupon由te 0时刻Benchmark利率决定，因此te 1的Coupon rate有-0.25%+4%则te 1的Coupon为1000×（-0.0025+0.04）= 37.50te 1的Coupon现金流加上Value现金流构成te 1的总现金流向te0折现(1112.73×0.5+1115.03×0.5+37.50)/(1-0.25%)=1154.27这个1154.27为债券的VN下面利用二叉树计算债券的CVA；te 4的Exposure为0.125×1120.80+0.375×1094.16+0.375×1076.31+0.125×1064.34=1087.07te 3的Exposure为0.125×1037.01+0.375×1037.94+0.375×1038.60+0.125×1039.05+0.250×84+0.5×69.49+0.250×59.77=1108.90te 2的Exposure为0.25×1074.21+0.5×1076.03+0.25×1077.30+61.18×0.5+54.20×0.5=1133.583te 1的Exposure为1112.73×0.5+1115.03×0.5+37.50=1151.38由以上Exposure数据，已知Recovery rate为25%，所以可以知道Recovery；再用Exposure减去Recovery可以得到Loss given fault (LG；本题 hazarrate为1.5%，则可以算出POS以及对应PO再用违约损失LG以违约概率PO到预期损失Expecteloss；Expecteloss通过折现因子求得PV(EL)；加总即得到债券的CVA；因此由债券的VN去其CVA可以的到Fair value1154.27 – 47.6019 = 1106.67；已知当前债券的市场价格为1054；则可以改债券是相对被低估的。浮动利率这种算一道题就得半个小时，还很可能错一点结果就都错了，性价比太低了，高估低估随便蒙一个正确率还有50%，还不浪费时间，这个知识点可以建议考生直接忽略随便选一个，以整个考试为视角收益是最大的。

NO.PZ2019011002000009 问题如下 BonC is a 4-yecorporate bon The bonis a floating rate bonanits coupon rate is the one-yebenchmark rate plus 4%. Assume the risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50%, anthe recovery rate is 25%.The current spot rates anforwarrates are shown in the table below:Li, a cret analyst in a wealth management firm, believes ththe future interest rate volatility is 20%.He constructea binomiinterest rate tree using his volatility estimation anthe current yielcurve.The binomiinterest rate tree is shown below:The market priof this floating rate bonis 1054 currently. Accorng to the information above, comparewith the bons fair value, the value of the bonis: A.Unrvalue B.Overvalue C.Fairly-value A is correct.考点使用二叉树对有风险的浮动利率债券进行估值解析本题是要计算Floating-rate bonFair value；首先需要用二叉树模型计算其VN有该浮动利率债券的Coupon为Benchmark rate加上4%，因此te 4的Coupon rate出现的情况有8.0804%+4%；5.4164%+4%；3.6307%+4%；2.4338%+4%因此te 4现金流的情况1000×(1+0.080804+0.04)=1120.801000×(1+0.054164+0.04)=1094.161000×(1+0.036307+0.04)=1076.311000×(1+0.024338+0.04)=1064.34由te 4的现金流和二叉树所示利率，可以折现求得te 3四个节点的Value:1120.80/1.080804=1037.011094.16/1.054164=1037.941076.31/1.036307=1038.601064.34/1.024338=1039.05由te 2的Benchmark利率可以知道在te 3三个节点Coupon rate出现的情况有4.3999%+4%；2.9493%+4%；1.9770%+4%因此te 3 Coupon现金流的情况1000×（0.043999+0.04）=841000×（0.029493+0.04）=69.491000×（0.019770+0.04）=59.77将te 3各个节点的Coupon加上te 3各个节点的Value构成te 3的总现金流，利用二叉树向te 2折现[(0.5×1037.01+0.5×1037.94)+84]/1.043999=1074.21[(0.5×1037.94+0.5×1038.60)+69.49]/1.029493=1076.03[(0.5×1038.60+0.5×1039.05)+59.77]/1.019770=1077.30te 2的两个节点的Coupon由te 1 Benchmark利率决定，因此te 1的Coupon rate出现的情况有2.1180%+4%；1.4197%+4%；因此te 2 coupon现金流的情况1000×（0.021180+0.04）= 61.181000×（0.014197+0.04）= 54.20te 2的Coupon现金流加上Value现金流构成te 2的总现金流向te 1折现(1074.21×0.5+1076.03×0.5+61.18)/(1+2.1180%)=1112.73(1076.03×0.5+1077.30×0.5+54.20)/(1+1.4197%)=1115.03te 1的Coupon由te 0时刻Benchmark利率决定，因此te 1的Coupon rate有-0.25%+4%则te 1的Coupon为1000×（-0.0025+0.04）= 37.50te 1的Coupon现金流加上Value现金流构成te 1的总现金流向te0折现(1112.73×0.5+1115.03×0.5+37.50)/(1-0.25%)=1154.27这个1154.27为债券的VN下面利用二叉树计算债券的CVA；te 4的Exposure为0.125×1120.80+0.375×1094.16+0.375×1076.31+0.125×1064.34=1087.07te 3的Exposure为0.125×1037.01+0.375×1037.94+0.375×1038.60+0.125×1039.05+0.250×84+0.5×69.49+0.250×59.77=1108.90te 2的Exposure为0.25×1074.21+0.5×1076.03+0.25×1077.30+61.18×0.5+54.20×0.5=1133.583te 1的Exposure为1112.73×0.5+1115.03×0.5+37.50=1151.38由以上Exposure数据，已知Recovery rate为25%，所以可以知道Recovery；再用Exposure减去Recovery可以得到Loss given fault (LG；本题 hazarrate为1.5%，则可以算出POS以及对应PO再用违约损失LG以违约概率PO到预期损失Expecteloss；Expecteloss通过折现因子求得PV(EL)；加总即得到债券的CVA；因此由债券的VN去其CVA可以的到Fair value1154.27 – 47.6019 = 1106.67；已知当前债券的市场价格为1054；则可以改债券是相对被低估的。 为啥这道题目在计算exposure的时候没有考虑coupon的不确定性的加权平均？？？

NO.PZ2019011002000009问题如下BonC is a 4-yecorporate bon The bonis a floating rate bonanits coupon rate is the one-yebenchmark rate plus 4%. Assume the risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50%, anthe recovery rate is 25%.The current spot rates anforwarrates are shown in the table below:Li, a cret analyst in a wealth management firm, believes ththe future interest rate volatility is 20%.He constructea binomiinterest rate tree using his volatility estimation anthe current yielcurve.The binomiinterest rate tree is shown below:The market priof this floating rate bonis 1054 currently. Accorng to the information above, comparewith the bons fair value, the value of the bonis:A.Unrvalue.Overvalue.Fairly-valueA is correct.考点使用二叉树对有风险的浮动利率债券进行估值解析本题是要计算Floating-rate bonFair value；首先需要用二叉树模型计算其VN有该浮动利率债券的Coupon为Benchmark rate加上4%，因此te 4的Coupon rate出现的情况有8.0804%+4%；5.4164%+4%；3.6307%+4%；2.4338%+4%因此te 4现金流的情况1000×(1+0.080804+0.04)=1120.801000×(1+0.054164+0.04)=1094.161000×(1+0.036307+0.04)=1076.311000×(1+0.024338+0.04)=1064.34由te 4的现金流和二叉树所示利率，可以折现求得te 3四个节点的Value:1120.80/1.080804=1037.011094.16/1.054164=1037.941076.31/1.036307=1038.601064.34/1.024338=1039.05由te 2的Benchmark利率可以知道在te 3三个节点Coupon rate出现的情况有4.3999%+4%；2.9493%+4%；1.9770%+4%因此te 3 Coupon现金流的情况1000×（0.043999+0.04）=841000×（0.029493+0.04）=69.491000×（0.019770+0.04）=59.77将te 3各个节点的Coupon加上te 3各个节点的Value构成te 3的总现金流，利用二叉树向te 2折现[(0.5×1037.01+0.5×1037.94)+84]/1.043999=1074.21[(0.5×1037.94+0.5×1038.60)+69.49]/1.029493=1076.03[(0.5×1038.60+0.5×1039.05)+59.77]/1.019770=1077.30te 2的两个节点的Coupon由te 1 Benchmark利率决定，因此te 1的Coupon rate出现的情况有2.1180%+4%；1.4197%+4%；因此te 2 coupon现金流的情况1000×（0.021180+0.04）= 61.181000×（0.014197+0.04）= 54.20te 2的Coupon现金流加上Value现金流构成te 2的总现金流向te 1折现(1074.21×0.5+1076.03×0.5+61.18)/(1+2.1180%)=1112.73(1076.03×0.5+1077.30×0.5+54.20)/(1+1.4197%)=1115.03te 1的Coupon由te 0时刻Benchmark利率决定，因此te 1的Coupon rate有-0.25%+4%则te 1的Coupon为1000×（-0.0025+0.04）= 37.50te 1的Coupon现金流加上Value现金流构成te 1的总现金流向te0折现(1112.73×0.5+1115.03×0.5+37.50)/(1-0.25%)=1154.27这个1154.27为债券的VN下面利用二叉树计算债券的CVA；te 4的Exposure为0.125×1120.80+0.375×1094.16+0.375×1076.31+0.125×1064.34=1087.07te 3的Exposure为0.125×1037.01+0.375×1037.94+0.375×1038.60+0.125×1039.05+0.250×84+0.5×69.49+0.250×59.77=1108.90te 2的Exposure为0.25×1074.21+0.5×1076.03+0.25×1077.30+61.18×0.5+54.20×0.5=1133.583te 1的Exposure为1112.73×0.5+1115.03×0.5+37.50=1151.38由以上Exposure数据，已知Recovery rate为25%，所以可以知道Recovery；再用Exposure减去Recovery可以得到Loss given fault (LG；本题 hazarrate为1.5%，则可以算出POS以及对应PO再用违约损失LG以违约概率PO到预期损失Expecteloss；Expecteloss通过折现因子求得PV(EL)；加总即得到债券的CVA；因此由债券的VN去其CVA可以的到Fair value1154.27 – 47.6019 = 1106.67；已知当前债券的市场价格为1054；则可以改债券是相对被低估的。这题VN能用表1的spot rate 折现吗，一定要用二叉树吗？之前题库也有个类似的，那道题没用二叉树求VN直接用ytm求的。这题我用spot rate折现结果是1107.86889答案也是对的，和二叉树求的也差太多了