问题如下图：
选项：
A. 
B. 
C. 
D. 
解释：
老师，您好。这题不是很明白，cln本质上是一个cds吧。这个公式（pv payoff - pv spread）认同，但是题目的条件，这个公式还应该不能用吧。
之后解析又给了一个公式 discount yield = cs*duration这是哪里来的。
谢谢
品职答疑小助手雍 · 2018年10月03日
同学你好，首先这题里的cln是一个note，也就是一个债券，求的是债券的fair value。
按照答案的解析做法：先计算利差久期，spread duration=1/1.05+1/1.05^2+1/1.05^3=2.72，乘以spread的差额90-60=30bps，2.72*0.3%=0.81%，因为折价，所以是100*（1-0.81%）=99.19
另外我再跟你讲一个更容易理解的方法：这个债券现在的现金流是6笔，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。
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=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt), 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
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=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt), 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。
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=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt), 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. 老师第二个思路，不是很看得懂，感觉上他的思路是用C定价推到出来的价格，为什么直接求ration 在乘以 sprea差，没感觉出来这一步和公式有什么关系
没看懂题干，能一下吗
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=1Tkt(1−f)PVt)−s(∑t=1TSt−1PVt), 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