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小米魔女 Michelle Zhao · 2022年08月30日

请问这个r=3%是怎么出来的。

  1. CFA II
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ201812310200000101

问题如下：

The market price of bond B1 is€875. The bond is:

选项：

A.

fairly valued.

B.

overvalued.

C.

undervalued.

解释：

B is correct.

The following table shows that the credit valuation adjustment (CVA) for the bond is

€36.49, the sum of the present values of expected loss. The steps taken to complete the table are as follows.

Step 1: Exposure at Date T is 1000 (1+r) 4−T , where r is 3%. That is, exposure is computed by discounting the face value of the bond using the risk-free rate and the number of years until maturity.

Step 2: Recovery = Exposure × Recovery rate

Step 3: Loss given default (LGD) = Exposure – Recovery

Step 4: Probability of default (POD) on Date 1 is 1.50%, the assumed hazard rate. The probability of survival (POS) on Date 1 is 98.50%.

For subsequent dates, POD is calculated as the hazard rate multiplied by the previous date’s POS.

For example, to determine the Date 2 POD (1.4775%), the hazard rate of (1.50%) is multiplied by the Date 1 POS (98.50%).

Step 5: POS in Dates 2–4 = POS in the previous year – POD

(That is, POS in Year T= POS in year [ T– 1] – POD in Year T.)

POS can also be 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 6: Expected loss = LGD × POD

Step 7: Discount factor (DF) for Date T is 1 (1+r) T , where r is 3%.

Step 8: PV of expected loss = Expected loss × DF

Value of the bond if the bond were default free would be 1,000 × DF for Date 4 = €888.49.

Fair value of the bond considering CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00.

Because the market price of the bond (€875) is greater than the fair value of €852, B is correct.

A is incorrect because the market price of the bond differs from its fair value. C is incorrect because although the bond’s value if the bond were default free is greater than the market price, the bond has a risk of default, and CVA lowers its fair value to below the market price.

老师，如题请帮忙解答。谢谢

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1 个答案

pzqa015 · 2022年08月31日

嗨，努力学习的PZer你好：


在没有利率波动的假设下，国债利率是3%，所以要用3%折现。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ201812310200000101 问题如下 The market priof bonis€875. The bonis: fairly value overvalue unrvalue B is correct. The following table shows ththe cret valuation austment (CVfor the bonis €36.49, the sum of the present values of expecteloss. The steps taken to complete the table are follows. Step 1: Exposure te T is 1000 (1+r) 4−T , where r is 3%. This, exposure is computescounting the favalue of the bonusing the risk-free rate anthe number of years until maturity. Step 2: Recovery = Exposure × Recovery rate Step 3: Loss given fault (LG = Exposure – Recovery Step 4: Probability of fault (PO on te 1 is 1.50%, the assumehazarrate. The probability of surviv(POS) on te 1 is 98.50%. For subsequent tes, POis calculatethe hazarrate multipliethe previous te’s POS. For example, to termine the te 2 PO(1.4775%), the hazarrate of (1.50%) is multipliethe te 1 POS (98.50%). Step 5: POS in tes 2–4 = POS in the previous ye– POD (This, POS in YeT= POS in ye[ T– 1] – POin YeT.) POS calso be 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 6: Expecteloss = LG× POD Step 7: scount factor () for te T is 1 (1+r) T , where r is 3%. Step 8: PV of expecteloss = Expecteloss × Value of the bonif the bonwere fault free woul1,000 × for te 4 = €888.49. Fair value of the bonconsiring CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00. Because the market priof the bon(€875) is greater ththe fair value of €852, B is correct. A is incorrect because the market priof the bonffers from its fair value. C is incorrebecause although the bons value if the bonwere fault free is greater ththe market price, the bond ha risk of fault, anCVA lowers its fair value to below the market price. RT

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