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yanan · 2024年10月27日

解析公式没看懂

NO.PZ2024042601000057

问题如下:

Banko, Inc., entered into a $10 million notional, 7-year CDS as a protection buyer three years ago at a spread of 1.85%. The current 4-year CDS spread for the same reference entity is 2.30% based on the PV of expected payoff of 0.0312 per $1 notional. The value of the CDS to Banko, Inc., is closest to:

选项:

A.

−$55,000

B.

−$60,900

C.

+$61,000

D.

+$53,000

解释:

Recognize that the value of the CDS is calculated such that:

Current PV of expected payment = current PV of expected payoff = 0.0312

Using the current spread of 2.30%, the current PV of expected payments = s=0.312/0.023=1.3565

Applying this value to the initial CDS spread of 1.85% yields:

PV of expected payments = 0.0185*1.3565=0.0251

Value to the protection buyer = PV of expected payoff - PV of expected payments = 0.0312 - 0.0251 = 0.0061 per 1$ notional.

The swap value for the $10 million notional = 0.0061 × 10,000,000 = $61,000. Because the spread has widened, the protection buyer gains.

Using the current spread of 2.30%, the current PV of expected payments = s=0.312/0.023=1.3565

Applying this value to the initial CDS spread of 1.85% yields:

PV of expected payments = 0.0185*1.3565=0.0251


这两排这样计算的公式和理由是什么呢,麻烦讲解下

1 个答案

pzqa27 · 2024年10月28日

嗨,努力学习的PZer你好:


这个题目涉及信用违约掉期(CDS)的估值。

  • 保护买方:Banko, Inc. 作为保护买方,通过CDS支付保费(利差),以换取在参考实体违约时的赔偿。
  • 名义金额:CDS的基础金额,这里是1000万美元。
  • CDS利差:保护买方每年支付的保费,最初为1.85%,现在为2.30%。
  • 估值方法: pv(expected payoff)-pv(expected payment)

当前CDS

  • pv(expected payoff)为每1美元名义金额0.0312,这表示预计每1美元名义金额的赔付为0.0312。


pv(expected payment):

  • 使用当前利差(2.30%)计算保护买方的 expected payoff 现值: 根据原版书的例题的算法,当前如果新签一份合约 PV(expectedd payoff)=PV (expected payment), 现在PV(expected payoff)=0.0312, 而PV(expected payoff)可以认为是对spread根据权重折现,最后得到的表现式子一定是X*spread这样,现在spread是2.3,那么X*2.3=0.0312 X解之得1.3565
  • 接着,使用初始CDS利差(1.85%)计算 expected payments 现值: expected payments 现值=初始利差*X =0.0185×1.3565≈0.0251


计算保护买方的价值

  • CDS对Banko, Inc.的价值是当前预期支付现值与expected payoff现值之间的差: 保护买方的价值=预期支付现值−预期支付现值=0.0312−0.0251=0.0061 

计算总价值

  • 最后,计算1000万美元名义金额的总价值: 总价值=0.0061×10,000,000=61,000

由于CDS利差扩大(从1.85%增加到2.30%),Banko, Inc.作为保护买方从中受益,因此CDS的价值大约为61,000美元。

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