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杨木木 · 2021年02月15日

关于本题的VND

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NO.PZ201812310200000203

问题如下:

Based on Kowalski’s assumptions and Exhibits 2 and 3, the credit spread on the VraiRive bond is closest to:

选项:

A.

0.6949%.

B.

0.9388%.

C.

1.4082%.

解释:

C is correct. The credit spread can be calculated in three steps:
Step 1 Estimate the value of the three-year VraiRive bond assuming no default. Based on Kowalski’s assumptions and Exhibits 2 and 3, the value of the three-year VraiRive bond assuming no default is 100.0000.


Supporting calculations:
The bond value in each node is the value of next period’s cash flows discounted by the forward rate. For the three nodes on Date 2, the bond values are as follows:
105/1.081823 = 97.0584.
105/1.066991 = 98.4076.
105/1.054848 = 99.5404.
For the two nodes on Date 1, the two bond values are as follows:
[0.5 × (97.0584) + 0.5 × (98.4076) + 5.00]/1.060139 = 96.9052.
[0.5 × (98.4076) + 0.5 × (99.5404) + 5.00]/1.049238 = 99.0948.
Finally, for the node on Date 0, the bond value is
[0.5 × (96.9052) + 0.5 × (99.0948) + 5.00]/1.030000 = 100.0000.
Therefore, the VND for the VraiRive bond is 100.0000.

Step 2 Calculate the credit valuation adjustment (CVA), and then subtract the CVA from the VND from Step 1 to establish the fair value of the bond. The CVA equals the sum of the present values of each year’s expected loss and is calculated as follows:

Supporting calculations:
The expected exposures at each date are the bond values at each node, weighted by their risk-neutral probabilities, plus the coupon payment:
Date 1: 0.5 × (96.9052) + 0.5 × (99.0948) + 5.00 = 103.0000.
Date 2: 0.25 × (97.0584) + 0.5 × (98.4076) + 0.25 × (99.5404) + 5.00 = 103.3535.

Date 3: 105.0000
The loss given default (LGD) on each date is 2/3 of the expected exposure.
The probability of default (POD) on each date is as follows:
Date 1: 2%
Date 2: 2% × (100% – 2%) = 1.96%.
Date 3: 2% × (100% – 2%)2 = 1.9208%.
The discount factor on each date is 1/(1 + spot rate for the date) raised to the correct power.
Finally, the credit valuation adjustment each year is the product of the LGD times the POD times the discount factor, as shown in the last column of the table. The sum of the three annual CVAs is 3.7360.
So, the fair value of the VraiRive bond is the VND less the CVA, or VND – CVA = 100 – 3.7360 = 96.2640.
Step 3 Based on the fair value from Step 2, calculate the yield to maturity of the bond, and solve for the credit spread by subtracting the yield to maturity on the benchmark bond from the yield to maturity on the VraiRive bond. The credit spread is equal to the yield to maturity on the VraiRive bond minus the yield to maturity on the three-year benchmark bond (which is 5.0000%). Based on its fair value of 96.2640, the VraiRive bond’s yield to maturity (YTM) is 96.2640=5/(1+YTM)+5/(1+YTM)2+105/(1+YTM)3
Solving for YTM, the yield to maturity is 6.4082%. Therefore, the credit spread on the VraiRive bond is 6.4082% – 5.0000% = 1.4082%.

答案说:Based on Kowalski’s assumptions and Exhibits 2 and 3, the value of the three-year VraiRive bond assuming no default is 100.0000.


请问老师,这个题的VND = 100 一定要二叉树求出吗? 计算器CF0=0,CF1 = 5,CF2 = 5, CF3 = 105,I = 5,最后算出→NPV也是100.


还是说只要给出了二叉树,就不能用DCF的方法算,必须用二叉树,这里只是恰巧约等于100而已?

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吴昊_品职助教 · 2021年02月15日

同学你好:

计算VND也可以通过表格中的discount factor得到,乘以discount factor其实就是除以spot rate。用二叉树求VND和用spot rate求VND两种方法,两种方法求出来的VND都是一样的。

用二叉树求VND的好处是我们后面还要求CVA,在计算每一期的exposure的时候,也是需要求出每一个节点的value的。所以如果题目同时给出二叉树和spot rate,建议还是使用二叉树来算VND。

Pavel Korchagin · 2024年02月21日

exposure 可以用forward rate 求吗

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NO.PZ201812310200000203问题如下Baseon Kowalski’s assumptions anExhibits 2 an3, the cret spreon the VraiRive bonis closest to: A.0.6949%. B.0.9388%. C.1.4082%. C is correct. The cret spreccalculatein three steps:Step 1 Estimate the value of the three-yeVraiRive bonassuming no fault. Baseon Kowalski’s assumptions anExhibits 2 an3, the value of the three-yeVraiRive bonassuming no fault is 100.0000.Supporting calculations:The bonvalue in eano is the value of next perios cash flows scountethe forwarrate. For the three nos on te 2, the bonvalues are follows:105/1.081823 = 97.0584.105/1.066991 = 98.4076.105/1.054848 = 99.5404.For the two nos on te 1, the two bonvalues are follows:[0.5 × (97.0584) + 0.5 × (98.4076) + 5.00]/1.060139 = 96.9052.[0.5 × (98.4076) + 0.5 × (99.5404) + 5.00]/1.049238 = 99.0948.Finally, for the no on te 0, the bonvalue is[0.5 × (96.9052) + 0.5 × (99.0948) + 5.00]/1.030000 = 100.0000.Therefore, the VNfor the VraiRive bonis 100.0000.Step 2 Calculate the cret valuation austment (CVA), anthen subtrathe CVA from the VNfrom Step 1 to establish the fair value of the bon The CVA equals the sum of the present values of eayear’s expecteloss anis calculatefollows:Supporting calculations:The expecteexposures eate are the bonvalues eano, weightetheir risk-neutrprobabilities, plus the coupon payment:te 1: 0.5 × (96.9052) + 0.5 × (99.0948) + 5.00 = 103.0000.te 2: 0.25 × (97.0584) + 0.5 × (98.4076) + 0.25 × (99.5404) + 5.00 = 103.3535.te 3: 105.0000The loss given fault (LG on eate is 2/3 of the expecteexposure.The probability of fault (PO on eate is follows:te 1: 2%te 2: 2% × (100% – 2%) = 1.96%.te 3: 2% × (100% – 2%)2 = 1.9208%.The scount factor on eate is 1/(1 + spot rate for the te) raiseto the correpower.Finally, the cret valuation austment eayeis the proof the LGtimes the POtimes the scount factor, shown in the last column of the table. The sum of the three annuCVis 3.7360.So, the fair value of the VraiRive bonis the VNless the CVor VN– CVA = 100 – 3.7360 = 96.2640.Step 3 Baseon the fair value from Step 2, calculate the yielto maturity of the bon ansolve for the cret spresubtracting the yielto maturity on the benchmark bonfrom the yielto maturity on the VraiRive bon The cret spreis equto the yielto maturity on the VraiRive bonminus the yielto maturity on the three-yebenchmark bon(whiis 5.0000%). Baseon its fair value of 96.2640, the VraiRive bons yielto maturity (YTM) is 96.2640=5/(1+YTM)+5/(1+YTM)2+105/(1+YTM)3Solving for YTM, the yielto maturity is 6.4082%. Therefore, the cret spreon the VraiRive bonis 6.4082% – 5.0000% = 1.4082%.请问是否可以用 CF0=-100,CF1=5,CF2=5,CF3=105,求IRR算YTM3?还是直接用第三年的coupon rate就可以了?

2024-05-24 18:02 1 · 回答

NO.PZ201812310200000203 问题如下 Baseon Kowalski’s assumptions anExhibits 2 an3, the cret spreon the VraiRive bonis closest to: A.0.6949%. B.0.9388%. C.1.4082%. C is correct. The cret spreccalculatein three steps:Step 1 Estimate the value of the three-yeVraiRive bonassuming no fault. Baseon Kowalski’s assumptions anExhibits 2 an3, the value of the three-yeVraiRive bonassuming no fault is 100.0000.Supporting calculations:The bonvalue in eano is the value of next perios cash flows scountethe forwarrate. For the three nos on te 2, the bonvalues are follows:105/1.081823 = 97.0584.105/1.066991 = 98.4076.105/1.054848 = 99.5404.For the two nos on te 1, the two bonvalues are follows:[0.5 × (97.0584) + 0.5 × (98.4076) + 5.00]/1.060139 = 96.9052.[0.5 × (98.4076) + 0.5 × (99.5404) + 5.00]/1.049238 = 99.0948.Finally, for the no on te 0, the bonvalue is[0.5 × (96.9052) + 0.5 × (99.0948) + 5.00]/1.030000 = 100.0000.Therefore, the VNfor the VraiRive bonis 100.0000.Step 2 Calculate the cret valuation austment (CVA), anthen subtrathe CVA from the VNfrom Step 1 to establish the fair value of the bon The CVA equals the sum of the present values of eayear’s expecteloss anis calculatefollows:Supporting calculations:The expecteexposures eate are the bonvalues eano, weightetheir risk-neutrprobabilities, plus the coupon payment:te 1: 0.5 × (96.9052) + 0.5 × (99.0948) + 5.00 = 103.0000.te 2: 0.25 × (97.0584) + 0.5 × (98.4076) + 0.25 × (99.5404) + 5.00 = 103.3535.te 3: 105.0000The loss given fault (LG on eate is 2/3 of the expecteexposure.The probability of fault (PO on eate is follows:te 1: 2%te 2: 2% × (100% – 2%) = 1.96%.te 3: 2% × (100% – 2%)2 = 1.9208%.The scount factor on eate is 1/(1 + spot rate for the te) raiseto the correpower.Finally, the cret valuation austment eayeis the proof the LGtimes the POtimes the scount factor, shown in the last column of the table. The sum of the three annuCVis 3.7360.So, the fair value of the VraiRive bonis the VNless the CVor VN– CVA = 100 – 3.7360 = 96.2640.Step 3 Baseon the fair value from Step 2, calculate the yielto maturity of the bon ansolve for the cret spresubtracting the yielto maturity on the benchmark bonfrom the yielto maturity on the VraiRive bon The cret spreis equto the yielto maturity on the VraiRive bonminus the yielto maturity on the three-yebenchmark bon(whiis 5.0000%). Baseon its fair value of 96.2640, the VraiRive bons yielto maturity (YTM) is 96.2640=5/(1+YTM)+5/(1+YTM)2+105/(1+YTM)3Solving for YTM, the yielto maturity is 6.4082%. Therefore, the cret spreon the VraiRive bonis 6.4082% – 5.0000% = 1.4082%. 课上何老师好像说过这个,记不清了

2024-02-21 22:13 1 · 回答

NO.PZ201812310200000203 这里每一期的coupon rate分别是3%,4.2%,5%。为什么用二叉树算VN时候,每一期的coupon都是5%来算的? 之前好像做过一道题,每一期的coupon也是要分别计算的。有点晕。

2021-06-25 00:07 1 · 回答

这个benchmark yiel5%是哪里来的?题干里好像不是5%整

2020-03-21 19:31 1 · 回答