问一道题：NO.PZ2019011002000007 [ CFA II ]

NO.PZ2019011002000007 问题如下 BonB is a 4-yeannucoupon bonwith a pvalue of $1000, ancoupon rate of 6%. The risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50% anthe recovery rate is 25%.Li is a cret analyst in a wealth management firm. He is consiring a future interest rate volatility of 20%.The current spot rates anforwarrates are shown in the table below:He built a binomiinterest rate tree using his volatility estimation anthe current yielcurve. The Binomiinterest rate tree is shown below:Accorng to the information above, whis the fair value of Bon A.1098.14 B.1144.63 C.1251.35 A is correct考点使用二叉树对有风险的固定利率债券进行估值解析首先利用二叉树模型，计算VN(Value of the bonassuming No fault）; 得到债券的VN1144.63下面就要计算债券的CVA。第一步计算二叉树上每期的exposure，如te 4的exposure为1060;te 3的exposure为0.1250×980.75+0.3750×1005.54+0.3750×1022.86+0.1250×1034.81+60=1072.60te 2的exposure为0.25×1008.76+0.50×1043.43+0.25×1067.73+60=1100.84te 1的exposure为0.50×1063.57+0.50×1099.96+60=1141.76有了每一期的Exposure，可以计算LGLoss given fault），有公式LG= exposure × (1-recovery rate)已知Hazarrate为1.500%，则每一期的POS（Probability of survival）为(100%-1.5%)1=98.5%(100%-1.5%)2=97.0225%(100%-1.5%)3=95.5672%(100%-1.5%)4=94.1337%(100%-1.5%)5=92.7217%已知每一期的POS，则可以算出每一期的POProbability of fault）折现因子（）可以题干信息中获得；最终PV of expecteloss = Expecteloss ×。我们可以得到如下表格所以该债券的Fair value为1144.63 – 46.4915 = 1098.1385 算No faut的价格不是用spot rate和forwarrate一期一期折现算的么？和二叉树那张表有什么关系？exposure是怎么算的没看懂？有二叉树和一开始学的简单案例区别在哪里？二叉树主要是用来求什么的？

NO.PZ2019011002000007 问题如下 BonB is a 4-yeannucoupon bonwith a pvalue of $1000, ancoupon rate of 6%. The risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50% anthe recovery rate is 25%.Li is a cret analyst in a wealth management firm. He is consiring a future interest rate volatility of 20%.The current spot rates anforwarrates are shown in the table below:He built a binomiinterest rate tree using his volatility estimation anthe current yielcurve. The Binomiinterest rate tree is shown below:Accorng to the information above, whis the fair value of Bon A.1098.14 B.1144.63 C.1251.35 A is correct考点使用二叉树对有风险的固定利率债券进行估值解析首先利用二叉树模型，计算VN(Value of the bonassuming No fault）; 得到债券的VN1144.63下面就要计算债券的CVA。第一步计算二叉树上每期的exposure，如te 4的exposure为1060;te 3的exposure为0.1250×980.75+0.3750×1005.54+0.3750×1022.86+0.1250×1034.81+60=1072.60te 2的exposure为0.25×1008.76+0.50×1043.43+0.25×1067.73+60=1100.84te 1的exposure为0.50×1063.57+0.50×1099.96+60=1141.76有了每一期的Exposure，可以计算LGLoss given fault），有公式LG= exposure × (1-recovery rate)已知Hazarrate为1.500%，则每一期的POS（Probability of survival）为(100%-1.5%)1=98.5%(100%-1.5%)2=97.0225%(100%-1.5%)3=95.5672%(100%-1.5%)4=94.1337%(100%-1.5%)5=92.7217%已知每一期的POS，则可以算出每一期的POProbability of fault）折现因子（）可以题干信息中获得；最终PV of expecteloss = Expecteloss ×。我们可以得到如下表格所以该债券的Fair value为1144.63 – 46.4915 = 1098.1385 老师请问 te2的PV是怎么求出来的呢？

NO.PZ2019011002000007 问题如下 BonB is a 4-yeannucoupon bonwith a pvalue of $1000, ancoupon rate of 6%. The risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50% anthe recovery rate is 25%.Li is a cret analyst in a wealth management firm. He is consiring a future interest rate volatility of 20%.The current spot rates anforwarrates are shown in the table below:He built a binomiinterest rate tree using his volatility estimation anthe current yielcurve. The Binomiinterest rate tree is shown below:Accorng to the information above, whis the fair value of Bon A.1098.14 B.1144.63 C.1251.35 A is correct考点使用二叉树对有风险的固定利率债券进行估值解析首先利用二叉树模型，计算VN(Value of the bonassuming No fault）; 得到债券的VN1144.63下面就要计算债券的CVA。第一步计算二叉树上每期的exposure，如te 4的exposure为1060;te 3的exposure为0.1250×980.75+0.3750×1005.54+0.3750×1022.86+0.1250×1034.81+60=1072.60te 2的exposure为0.25×1008.76+0.50×1043.43+0.25×1067.73+60=1100.84te 1的exposure为0.50×1063.57+0.50×1099.96+60=1141.76有了每一期的Exposure，可以计算LGLoss given fault），有公式LG= exposure × (1-recovery rate)已知Hazarrate为1.500%，则每一期的POS（Probability of survival）为(100%-1.5%)1=98.5%(100%-1.5%)2=97.0225%(100%-1.5%)3=95.5672%(100%-1.5%)4=94.1337%(100%-1.5%)5=92.7217%已知每一期的POS，则可以算出每一期的POProbability of fault）折现因子（）可以题干信息中获得；最终PV of expecteloss = Expecteloss ×。我们可以得到如下表格所以该债券的Fair value为1144.63 – 46.4915 = 1098.1385 这样算EL不是很复杂吗？用EXPOSURE*(1-RR)*lo接算是否可以，比如第四期就是1060*0.75*1.4335%=11.7963

NO.PZ2019011002000007问题如下BonB is a 4-yeannucoupon bonwith a pvalue of $1000, ancoupon rate of 6%. The risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50% anthe recovery rate is 25%.Li is a cret analyst in a wealth management firm. He is consiring a future interest rate volatility of 20%.The current spot rates anforwarrates are shown in the table below:He built a binomiinterest rate tree using his volatility estimation anthe current yielcurve. The Binomiinterest rate tree is shown below:Accorng to the information above, whis the fair value of BonB?A.1098.14B.1144.63C.1251.35A is correct考点使用二叉树对有风险的固定利率债券进行估值解析首先利用二叉树模型，计算VN(Value of the bonassuming No fault）; 得到债券的VN1144.63下面就要计算债券的CVA。第一步计算二叉树上每期的exposure，如te 4的exposure为1060;te 3的exposure为0.1250×980.75+0.3750×1005.54+0.3750×1022.86+0.1250×1034.81+60=1072.60te 2的exposure为0.25×1008.76+0.50×1043.43+0.25×1067.73+60=1100.84te 1的exposure为0.50×1063.57+0.50×1099.96+60=1141.76有了每一期的Exposure，可以计算LGLoss given fault），有公式LG= exposure × (1-recovery rate)已知Hazarrate为1.500%，则每一期的POS（Probability of survival）为(100%-1.5%)1=98.5%(100%-1.5%)2=97.0225%(100%-1.5%)3=95.5672%(100%-1.5%)4=94.1337%(100%-1.5%)5=92.7217%已知每一期的POS，则可以算出每一期的POProbability of fault）折现因子（）可以题干信息中获得；最终PV of expecteloss = Expecteloss ×。我们可以得到如下表格所以该债券的Fair value为1144.63 – 46.4915 = 1098.1385请问每一期的po么计算呢？可否演示一下

NO.PZ2019011002000007问题如下BonB is a 4-yeannucoupon bonwith a pvalue of $1000, ancoupon rate of 6%. The risk-neutrprobability of fault (the hazarrate) for eate for the bonis 1.50% anthe recovery rate is 25%.Li is a cret analyst in a wealth management firm. He is consiring a future interest rate volatility of 20%.The current spot rates anforwarrates are shown in the table below:He built a binomiinterest rate tree using his volatility estimation anthe current yielcurve. The Binomiinterest rate tree is shown below:Accorng to the information above, whis the fair value of BonB?A.1098.14B.1144.63C.1251.35A is correct考点使用二叉树对有风险的固定利率债券进行估值解析首先利用二叉树模型，计算VN(Value of the bonassuming No fault）; 得到债券的VN1144.63下面就要计算债券的CVA。第一步计算二叉树上每期的exposure，如te 4的exposure为1060;te 3的exposure为0.1250×980.75+0.3750×1005.54+0.3750×1022.86+0.1250×1034.81+60=1072.60te 2的exposure为0.25×1008.76+0.50×1043.43+0.25×1067.73+60=1100.84te 1的exposure为0.50×1063.57+0.50×1099.96+60=1141.76有了每一期的Exposure，可以计算LGLoss given fault），有公式LG= exposure × (1-recovery rate)已知Hazarrate为1.500%，则每一期的POS（Probability of survival）为(100%-1.5%)1=98.5%(100%-1.5%)2=97.0225%(100%-1.5%)3=95.5672%(100%-1.5%)4=94.1337%(100%-1.5%)5=92.7217%已知每一期的POS，则可以算出每一期的POProbability of fault）折现因子（）可以题干信息中获得；最终PV of expecteloss = Expecteloss ×。我们可以得到如下表格所以该债券的Fair value为1144.63 – 46.4915 = 1098.1385老师请问 算exposure的时候我理解要加上当期的60coupon，但是用来算weighteaverage的数字 用的是已经加过60的数字，为什么算完weighteaverage最后还要再加60呢？ exposure的amount是前一年折现过来的weighteaverage amount 加 当期的coupon。答案里的算法是前一年折现过来的amount 加coupon算出一个WA，然后再加一个coupon，那岂不是coupon算了两次吗？