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还是星宇好 · 2020年10月19日

问一道题：NO.PZ2016082406000073

  1. FRM II
  2. Credit Risk Measurement And Management

问题如下：

A three-year credit-linked note (CLN) with underlying company Z has a LIBOR+60bp semiannual coupon. The face value of the CLN is USD 100. LIBOR is 5% for all maturities. The current three-year CDS spread for company Z is 90bp. The fair value of the CLN is closest to

选项：

A.

USD 100.00

B.

USD 111.05

C.

USD 101.65

D.

USD 99.19

解释：

ANSWER: D

Because the current CDS spread is greater than the coupon, the CLN must be selling at a discount. The only solution is d. More precisely, we can use the spread duration from Equation: V=(PV Payoff)−s(PV Spread)=(∑t=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt)V={(\text{PV Payoff})}-s(\text{PV Spread})={(\sum_{t=1}^Tk_t{(1-f)}{\text{PV}}_t)}-s{(\sum_{t=1}^TS_{t-1}{\text{PV}}_t)}, which is the sum of the present value factor over three years. Assuming a flat term structure,this is ∑PVt=0.952+0.907+0.864=2.72\sum PV_t=0.952+0.907+0.864=2.72 years. Multiplying by (90-60) = 30bp gives a fall of 0.81%,which gives $99.19.

老师第二个思路，不是很看得懂，感觉上他的思路是用CDS定价推到出来的价格，为什么直接求duration 在乘以 spread的差，没感觉出来这一步和公式有什么关系

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1 个答案

小刘_品职助教 · 2020年10月19日

同学你好，

是用利差分别进行折现，感觉跟这个公式确实没特别大的关系，这段spread durtaion 是在用无风险因子进行折现后汇总0.952+0.907+0.864=2.72 years。感觉有点给这段折现一个定义的意思。

个人建议还是用现金流折现做，2.8,2.8,2.8,2.8,2.8,102.8。题目说真实的spread是5%+90bps=5.9%，直接按这个折现率折现（rate=2.95%，N=6，pmt=2.8，fv=100）得到PV=99.19。

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NO.PZ2016082406000073 A three-yecret-linkenote (CLN) with unrlying company Z ha LIBOR+60semiannucoupon. The favalue of the CLN is US100. LIBOR is 5% for all maturities. The current three-yeC sprefor company Z is 90bp. The fair value of the CLN is closest to US100.00 US111.05 US101.65 US99.19 ANSWER: Because the current C spreis greater ththe coupon, the CLN must selling a scount. The only solution is More precisely, we cuse the spreration from Equation: V=(PV Payoff)−s(PV Sprea=(∑t=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt)V={(\text{PV Payoff})}-s(\text{PV Sprea)={(\sum_{t=1}^Tk_t{(1-f)}{\text{PV}}_t)}-s{(\sum_{t=1}^TS_{t-1}{\text{PV}}_t)}V=(PV Payoff)−s(PV Sprea=(∑t=1T​kt​(1−f)PVt​)−s(∑t=1T​St−1​PVt​), whiis the sum of the present value factor over three years. Assuming a flterm structure,this is ∑PVt=0.952+0.907+0.864=2.72\sum PV_t=0.952+0.907+0.864=2.72∑PVt​=0.952+0.907+0.864=2.72 years. Multiplying (90-60) = 30gives a fall of 0.81%,whigives $99.19. 这题到底要怎么做？完全无法理解，请老师讲的更基础些。 我看之前老师说将CLN当作一个boncoupon就是5.6%，但是c sprea5.9%。 然后我就不知道怎么做了

2021-04-07 00:01 1 · 回答

NO.PZ2016082406000073 A three-yecret-linkenote (CLN) with unrlying company Z ha LIBOR+60semiannucoupon. The favalue of the CLN is US100. LIBOR is 5% for all maturities. The current three-yeC sprefor company Z is 90bp. The fair value of the CLN is closest to US100.00 US111.05 US101.65 US99.19 ANSWER: Because the current C spreis greater ththe coupon, the CLN must selling a scount. The only solution is More precisely, we cuse the spreration from Equation: V=(PV Payoff)−s(PV Sprea=(∑t=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt)V={(\text{PV Payoff})}-s(\text{PV Sprea)={(\sum_{t=1}^Tk_t{(1-f)}{\text{PV}}_t)}-s{(\sum_{t=1}^TS_{t-1}{\text{PV}}_t)}V=(PV Payoff)−s(PV Sprea=(∑t=1T​kt​(1−f)PVt​)−s(∑t=1T​St−1​PVt​), whiis the sum of the present value factor over three years. Assuming a flterm structure,this is ∑PVt=0.952+0.907+0.864=2.72\sum PV_t=0.952+0.907+0.864=2.72∑PVt​=0.952+0.907+0.864=2.72 years. Multiplying (90-60) = 30gives a fall of 0.81%,whigives $99.19. 就是答案说应该拿来折现的利率应该是C的利率，这是为啥呢。 .用来折现的利率不是应该拿市场利率也就是Libor的利率吗，即5%。为什么要用C一个金融产品的利率（而非市场利率）来折现呢。

2021-03-13 22:00 1 · 回答

没看懂题干，能一下吗

2020-08-16 18:24 1 · 回答

A three-yecret-linkenote (CLN) with unrlying company Z ha LIBOR+60semiannucoupon. The favalue of the CLN is US100. LIBOR is 5% for all maturities. The current three-yeC sprefor company Z is 90bp. The fair value of the CLN is closest to US100.00 US111.05 US101.65 US99.19 ANSWER: Because the current C spreis greater ththe coupon, the CLN must selling a scount. The only solution is More precisely, we cuse the spreration from Equation: V=(PV Payoff)−s(PV Sprea=(∑t=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt)V={(\text{PV Payoff})}-s(\text{PV Sprea)={(\sum_{t=1}^Tk_t{(1-f)}{\text{PV}}_t)}-s{(\sum_{t=1}^TS_{t-1}{\text{PV}}_t)}V=(PV Payoff)−s(PV Sprea=(∑t=1T​kt​(1−f)PVt​)−s(∑t=1T​St−1​PVt​), whiis the sum of the present value factor over three years. Assuming a flterm structure,this is ∑PVt=0.952+0.907+0.864=2.72\sum PV_t=0.952+0.907+0.864=2.72∑PVt​=0.952+0.907+0.864=2.72 years. Multiplying (90-60) = 30gives a fall of 0.81%,whigives $99.19. 请问为什么C比coupon大，CLN就是折价的，谢谢

2020-04-04 11:49 1 · 回答