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yuqijeffery · 2022年07月17日

请问像fixed coupon直接加在exposure上就行了?浮动coupon要直接算在债券价格里,然后直接加权就可以了?

NO.PZ2019011002000009

问题如下:

Bond C is a 4-year corporate bond. The bond is a floating rate bond and its coupon rate is the one-year benchmark rate plus 4%. Assume the risk-neutral probability of default (the hazard rate) for each date for the bond is 1.50%, and the recovery rate is 25%.

The current spot rates and forward rates are shown in the table below:

Li, a credit analyst in a wealth management firm, believes that the future interest rate volatility is 20%.

He constructed a binomial interest rate tree by using his volatility estimation and the current yield curve.

The binomial interest rate tree is shown below:

The market price of this floating rate bond is 1054 currently. According to the information above, compared with the bond’s fair value, the value of the bond is:

选项:

A.

Undervalued

B.

Overvalued

C.

Fairly-valued

解释:

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 bond的Fair value;首先需要用二叉树模型计算其VND,有:

该浮动利率债券的Coupon为Benchmark rate加上4%,因此Date 4的Coupon rate出现的情况有:

8.0804%+4%;5.4164%+4%;3.6307%+4%;2.4338%+4%

因此Date 4现金流的情况:

1000×(1+0.080804+0.04)=1120.80

1000×(1+0.054164+0.04)=1094.16

1000×(1+0.036307+0.04)=1076.31

1000×(1+0.024338+0.04)=1064.34

由Date 4的现金流和二叉树所示利率,可以折现求得Date 3四个节点的Value:

1120.80/1.080804=1037.01

1094.16/1.054164=1037.94

1076.31/1.036307=1038.60

1064.34/1.024338=1039.05

由Date 2的Benchmark利率可以知道在Date 3三个节点Coupon rate出现的情况有:

4.3999%+4%;2.9493%+4%;1.9770%+4%

因此Date 3 Coupon现金流的情况:

1000×(0.043999+0.04)=84

1000×(0.029493+0.04)=69.49

1000×(0.019770+0.04)=59.77

将Date 3各个节点的Coupon加上Date 3各个节点的Value构成Date 3的总现金流,利用二叉树向Date 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=1077.30

Date 2的两个节点的Coupon由Date 1 Benchmark利率决定,因此Date 1的Coupon rate出现的情况有:

2.1180%+4%;1.4197%+4%;

因此Date 2 coupon现金流的情况:

1000×(0.021180+0.04)= 61.18

1000×(0.014197+0.04)= 54.20

Date 2的Coupon现金流加上Value现金流构成Date 2的总现金流向Date 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%)=1115.03

Date 1的Coupon由Date 0时刻Benchmark利率决定,因此Date 1的Coupon rate有:

-0.25%+4%

则Date 1的Coupon为:

1000×(-0.0025+0.04)= 37.50

Date 1的Coupon现金流加上Value现金流构成Date 1的总现金流向Date0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VND;下面利用二叉树计算债券的CVA;

Date 4的Exposure为:

0.125×1120.80+0.375×1094.16+0.375×1076.31

+0.125×1064.34=1087.07

Date 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=1108.90

Date 2的Exposure为:

0.25×1074.21+0.5×1076.03+0.25×1077.30

+61.18×0.5+54.20×0.5=1133.583

Date 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 default (LGD);本题 hazard rate为1.5%,则可以算出POS以及对应POD;再用违约损失LGD乘以违约概率POD得到预期损失Expected loss;Expected loss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VND减去其CVA可以的到Fair value:

1154.27 – 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。

请问像fixed coupon直接加在exposure上就行了?浮动coupon要直接算在债券价格里,然后直接加权就可以了?

1 个答案
已采纳答案

pzqa015 · 2022年07月18日

嗨,从没放弃的小努力你好:


fixed bond的coupon只放到P=∑CF/(1+y)的分子里,float bond除了分子外,还要在分母加上每一期的float rate,初次之外,剩下的解题过程float rate bond与fixed rate bond是一样的。

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加油吧,让我们一起遇见更好的自己!

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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

2024-03-04 16:40 1 · 回答

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2023-10-12 20:35 1 · 回答

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。

2023-09-07 13:00 1 · 回答

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???

2023-07-29 12:12 1 · 回答

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

2023-04-13 20:18 1 · 回答