# How does one make money from CVA (Credit Valuation Adjustment)?

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!

• 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. – dm63 Mar 9 at 23:05

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.