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RyanR · 2023年11月09日

我怎么理解这个套利的收益是buy bond还是short bond

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2020033002000062

问题如下：

A six-year CDS on a AAA-rated issuer is offered at 100bp with semiannual payments assuming no couterparty risk. The annualized LIBOR rate paid every six months is 4.8% for all maturities.If the yield on a six-year annual coupon bond of this issuer is 7%, is there any

arbitrage opportunity? If yes, how much is the return of the arbitrage strategy?

选项：

A.

No, there is no arbitrage opportunity.

B.

Yes, buy the bond and the CDS with a risk-free gain of 2.2%.

C.

Yes, buy the bond and the CDS with a risk-free gain of 1.2%.

D.

Yes, short the bond and sell CDS protection with a risk-free gain of 1.2%.

解释：

C is correct.

考点：CDS

解析：

Because LIBOR is flat, the fixed-coupon yield is also 4.8%, creating a spread of 700−480=220bp700-480=220bp on the bond. Going long the bond and short credit via buying the CDS yields an annual profit of 220−100=120bp220-100=120bp.

能看懂一直到，我买债券是能赚2.2%（risk premium），然后这个2.2里面有1通过CDS转移出去了。

所以是应该考虑，我还剩1.2%损失的风险，还是应该考虑我还能赚1.2%？


知道CDS的定价是通过无套利原理来定价的，但是没有理解到，题目这种情况是怎么个套利法？

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1 个答案

DD仔_品职助教 · 2023年11月10日

嗨，从没放弃的小努力你好：


同学请具体看下面的解析：

题目说，六年期的AAA级的CDS，半年付息一次，coupon rate是1%，没有对手方风险。年化的LIBOR利率每半年付息一次利率是4.8%，对每个期限都一样。如果六年期的年化coupon bond的YTM是7%，请问是否存在套利机会？

因为LIBOR利率对于所有期限都一样，都是4.8%，六年期的coupon bond利率是7%，credit spread是7%-4.8%=2.2%，代表因为存在违约风险所获得的溢价是2.2%，这里我们默认LIBOR是一个rf，那也就是说投资债券可以获得2.2%的回报率。

而CDS相当于一个保险，这个保险的费率是1%，如果我卖一个CDS保险可以获得1%的收益率。

这俩产品一个收益2.2%，一个收益1%，那我肯定是买收益率高的bond，同时买一个CDS保险支付出去1%的费率，可以获得2.2%-1%=1.2%的套利差额。

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