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yanan · 2024年10月27日

解析公式没看懂

  1. FRM II
  2. Credit Risk Measurement And Management

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

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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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努力的时光都是限量版，加油！

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NO.PZ2024042601000057 问题如下 Banko, Inc., entereinto a $10 million notional, 7-yeC a protection buyer three years ago a spreof 1.85%. The current 4-yeC sprefor the same referenentity is 2.30% baseon the PV of expectepayoff of 0.0312 per $1 notional. The value of the C to Banko, Inc., is closest to: A.−$55,000 B.−$60,900 C.+$61,000 +$53,000 Recognize ththe value of the C is calculatesuthat:Current PV of expectepayment = current PV of expectepayoff = 0.0312Using the current spreof 2.30%, the current PV of expectepayments = s=0.312/0.023=1.3565Applying this value to the initiC spreof 1.85% yiel:PV of expectepayments = 0.0185*1.3565=0.0251Value to the protection buyer = PV of expectepayoff - PV of expectepayments = 0.0312 - 0.0251 = 0.0061 per 1$ notional.The swvalue for the $10 million notion= 0.0061 × 10,000,000 = $61,000. Because the sprehwine the protection buyer gains. 没看懂，这C的估值怎么这么怪？C buyer Value = PV(Payment) + PV(accrupayment) - PV(payoff)这题怎么没有按照这个公式来？

2024-10-27 11:20 2 · 回答