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Value of a Credit Default Swap

QuantMan2318

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Hi @David Harper CFA FRM

Good to contact you after a while.

I had a question which may be relevant to the folks studying credit risk here as well, I had this after I was studying for the CFA

While valuing CDS, we have something called the CDS spread - is this equal or equivalent to the CVA?

And again, there is something called value of the credit exposure in the CDS which is basically the difference between the Risky Bond and the Risk free Bond, I cannot find this to be any different from a CVA

I would like to know your thoughts on this
 

QuantMan2318

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David Harper CFA FRM

David Harper CFA FRM
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Hi @QuantMan2318 Good to hear from you! :) I hope you are doing well. To be honest, I don't quite grok @ami44 's thread in particular in the way that CVA is mixed with CDS (I only read it once, so it certainly can be my misunderstanding); as you say ami44 appears to be "one who has both practical and theoretical knowledge of these things" so I will assume i need to re-read it.

However, on a more basic level, my answer is: no, CVA is not equivalent to the CDS spread (although they are superficially similar in the sense they both price credit risk).

Consider the CDS: a protection buyer is long a CDS that is written by its counterparty, the protection seller. The CDS references, let's say, Acme Corporate's Bond. If we perform a textbook valuation by pricing the CDS spread (e.g. Hulll Chapter 25), what are we doing? We are solving for the CDS spread that equates the PV of premium payments (paid by the long CDS) to the PV of contingent payoff (paid by the short CDS in the contingency of a credit event). The key but not only variable is the reference's (Acme's bond in my example) default probability, and the spread is a measure of the reference's (Acme's bond) default risk not the protection seller's! Before the credit crisis, this CDS valuation was present in the syllabus and nobody really talked about the credit risk of the protection seller! This valuation implicitly assumes (assumed) a 100% probability that the short CDS will make the contingent payment, if required. That is, we routinely valued the CDS implicitly without any CVA adjustment.

The CVA is the the price of counterparty credit risk. So we can incorporate CVA by adjusting the CDS spread up/down to account for the counterparty exposure. If the CDS seller is more risky (or if there exists wrong-way risk, right?, that is adverse correlation between CDS seller and the reference), then the CDS spread would be reduced by the CVA (the CDS buyer is less willing to pay the "premium" when there is some risk that the derivative contract's payoff will not be honored).

In this way, I think the CDS spread refers to the credit risk of the reference (aka, the underlying referenced by the derivative contract) while the CVA prices the credit risk of the CDS counterparty (aka, the derivative counterparty), and interestingly, they may not be independent. I hope that's helpful, talk to you soon!
 
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QuantMan2318

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<QUOTE>In this way, I think the CDS spread refers to the credit risk of the reference (aka, the underlying referenced by the derivative contract) while the CVA prices the credit risk of the CDS counterparty (aka, the derivative counterparty), and interestingly, they may not be independent. I hope that's helpful, talk to you soon!</QUOTE>

Think this covers it up quite neatly, Thank you
 
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