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很内向吃饱了也不说一直吃 · 2025年04月24日

根据EL求PV(EL)用的折现率

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NO.PZ202304070100009103

问题如下:

Ibarra performs the analysis assuming an upward-sloping yield curve and volatile interest rates. Exhibit 2 provides the data on annual payment benchmark government bonds. She uses this data to construct a binomial interest rate tree (shown in Exhibit 3) based on an assumption of future interest rate volatility of 20%.

Exhibit 3. One-Year Binomial Interest Rate Tree for 20% Volatility


As previously mentioned, Ibarra is considering a future interest rate volatility of 20% and an upward-sloping yield curve, as shown in Exhibit 2. Based on her analysis, the fair value of bond B2 is closest to:

选项:

A.

€1,101.24.

B.

€1,141.76.

C.

€1,144.63.

解释:

Correct Answer: A

The following tree shows the valuation assuming no default of bond B2, which pays a 6% annual coupon.


The scheduled year-end coupon and principal payments are placed to the right of each forward rate in the tree. For example, the Date 4 values are the principal plus the coupon of 60. The following are the four Date 3 values for the bond, shown above the interest rate at each node:

€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 Date 2 values:


So, the value of the bond assuming no default (VND) is 1,144.63. This value could also have been obtained more directly using the benchmark discount 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 binomial interest rate tree to obtain the VND is that the same tree is used to calculate the expected exposure to default loss. The credit valuation adjustment table is now prepared following these steps:

Step 1: Compute the expected exposures as described in the following, using the binomial interest rate tree prepared earlier.

The expected exposure for Date 4 is €1,060.

The expected exposure for Date 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 Date 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 Date 1 is:

[(0.50 × €1,063.57) + (0.50 × €1,099.96)] + 60 = €1,141.76.

Step 2: LGD = Exposure × (1 – Recovery rate)

Step 3: The initial POD, also known as the hazard rate, is provided as 1.50%. For subsequent dates, POD is calculated as the hazard rate multiplied by the previous dates’ POS.

For example, to determine the Date 2 POD (1.4775%), the hazard rate (1.5000%) is multiplied by the Date 1 POS (98.5000%).

Step 4: POS is determined by subtracting the hazard rate from 100% and raising 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: Expected loss = LGD × POD

Step 6: Discount factors (DF) in Year T are obtained from Exhibit 2.

Step 7: PV of expected loss = Expected loss × DF


Fair value of the bond considering CVA = €1,144.63 – CVA = €1,144.63 – €43.39 = €1,101.24.

老师,请问一下:

1.最后一步根据EL求PV(EL)用的折现率是【par curve for annual payment benchmark government bonds】表格里第一列数据,为什么不直接用前面题目里的rf 3%呢?

2.这种代入(1+S1)、(1+S2)^2、(1+S3)^3计算方法类似于前面第一章节的:每年不同Spot rateS1 S2 S3 S4求Value的方法吗?

3.这种给出【par curve for annual payment benchmark government bonds】表格的题型在考试里常见嘛?请问有什么方法能够在不同情况下诸多信息里捕捉需要用到的折现率呢?谢谢!

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NO.PZ202304070100009103问题如下 Ibarra performs the analysis assuming upwarsloping yielcurve anvolatile interest rates. Exhibit 2 provis the ta on annupayment benchmark government bon. She uses this ta to construa binomiinterest rate tree (shown in Exhibit 3) baseon assumption of future interest rate volatility of 20%.Exhibit 3. One-YearBinomiInterest Rate Tree for 20% Volatilitypreviously mentione Ibarra is consiring a future interest rate volatility of 20% anupwarsloping yielcurve, shown in Exhibit 2. Baseon her analysis, the fair value of bonis closest to: A.€1,101.24.B.€1,141.76.C.€1,144.63. CorreAnswer: AThe following tree shows the valuation assuming no fault of bonB2, whipays a 6% annucoupon.The scheleyear-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 eano:€1,060/1.080804 = €980.75€1,060/1.054164 = €1,005.54€1,060/1.036307 = €1,022.86€1,060/1.024338 = €1,034.81These are the three te 2 values: 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 preparefollowing these steps:Step 1: Compute the expecteexposures scribein the following, using the binomiinterest rate tree prepareearlier.The expecteexposure for te 4 is €1,060.The expecteexposure 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 expecteexposure for te 2 is:[(0.25 × €1,008.76) + (0.50 × €1,043.43) + (0.25 × €1,067.73)] + €60 = €1,100.84.The expecteexposure 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 multipliethe 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× POtep 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. 在计算VN每个时间节点使用的概率是0.5,而在计算CVA时时间节点概率不是用0.5呢?为什么两个概率使用的不一样?

2024-03-31 12:20 1 · 回答