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kevinzhu · 2021年04月02日

discount factor

  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.

discount factor怎么算出来的?

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2 个答案

WallE_品职答疑助手 · 2021年04月02日

嗨，努力学习的PZer你好：


表二题目给的。

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加油吧，让我们一起遇见更好的自己！

Moon · 2021年09月08日

这个应该是用3%贴现的折现因子吧，不是表二题目给的

WallE_品职答疑助手 · 2021年04月02日

嗨，爱思考的PZer你好：



公式如上，



以这个为例子，

DF=1/(1+2.2953%)^4=0.913224


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虽然现在很辛苦，但努力过的感觉真的很好，加油！

kevinzhu · 2021年04月02日

2.2953%是哪里来的

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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

2024-08-09 15:14 1 · 回答

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