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I am new to Quantitative Finance but have been doing a lot of reading on Counterparty Credit Risk.

I understand the definition of CVA being:

"the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default."

I understand the Positive and Negative Credit Exposure due to defaulting Counterparties. I mostly understand the CVA Formula being:

$CVA =\int_{0}^{T} \! EE * (t) dPD(0,t)\,\mathrm{d}t.$

My question is, How does one (a firm, a bank...) make money from CVA trades? If all CVA is, is the expected loss of a counterparty defaulting, how is that possible to make money on these trades?

Can someone provide a basic vanilla example of how this is possible. Thanks!

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  • $\begingroup$ The literal answer to the question of how to make money, is: charge more than the theoretical value, then hedge using the method of @Daniel Olivaw. $\endgroup$ – dm63 Mar 9 at 23:05
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Assuming zero recovery, let $\mathcal{C}$ be a counterparty you are facing on a derivative deal with value $V(t)$ and maturity $T$ such that $V(t)\geq 0$, for example an option. Let $CDS_\mathcal{C}(t,T)$ be the value at $t$ of a unit-notional CDS on $\mathcal{C}$ with maturity $T$. Then with the portfolio $\pi(t)=V(t)CDS_\mathcal{C}(t,T)$, namely a CDS trade with notional $V(t)$ (thus you need continuous rebalancing), you can hedge your risk of counterparty default and monetize CVA.

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You’re missing an important term in your expression for CVA, the recoverability of assets in the case of default. Since this value can be difficult to estimate, it’s possible to incorrectly compute CVA. In the case where you know recoverability to be higher than what the market thinks it is, you might become a seller of credit default swaps.

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