# CVA using difference between 2 counterparty's spreads

The approximation to calculate CVA as a spread is $CVA = Spread * Expected$ $Exposure$. I assume this means the counterparty's spread over a proxy for the risk free rate such as LIBOR or OIS. Is this an incorrect understanding?

I came across an FRM exam practice question created by GARP (the entity that runs the exam) which gave a scenario where both the bank and its counterparty experienced spread widenings due to rating downgrades. Where the banks spread went from 20bps to 150bps and its counterparty's spread went from 130bps to 170bps. The CVA a was given by (170-150)*Expected Exposure and was a reduction from the previous CVA of (130-20)*Expected Exposure. (Note, there is an assumption to ignore DVA)

This doesn't make sense to me. The counterparty to the bank suffered a downgrade and a resulting spread widening yet the CVA charge decreases?

I can't share the exact question, but here is essentially what it was

This was the question:

Foo Company is a frequent user of swaps with Acme Bank. Acme bank was recently downgraded from a rating of AA- to A+ and at the same time, Foo Company was downgraded from A to A-. As a result of the downgrades, the credit spread for Acme bank increased from 20bps to 150bps, and the credit spread for Foo Company increased from 130bps to 170 bps. The question asks what realistic changes the counterparties can request to their CVA charge, given a set of multiple choice.

Because Foo Company has a lower credit rating than the bank, it would typically pay a CVA charge which would be a function of the relative credit spreads between the two entities. As the the credit spread between the two has narrowed after the downgrade to only 20bps, Foo Company can request a reduction in their CVA charge.

• It is hard to understand since we do not have the context. Is those practice questions openly available? – Gordon Nov 22 '15 at 15:40
• I'll try and find it, they are not publicly available – AfterWorkGuinness Nov 22 '15 at 15:41
• I've updated the question. – AfterWorkGuinness Nov 22 '15 at 16:00
• It appears to me that the DVA is considered. Then the charge is basically CVA - DVA. As the downgraded spreads are now closer than they were previously, the bilateral CVA is reduced. – Gordon Nov 22 '15 at 16:41

What GARP considered for the question is a first-to-default CVA, meaning that the bank looks at what it expects to lose if its counterparty defaults before it does. In this case the formula would be: $\mathrm{CVA}=\left(Spread_{Counterparty} - Spread_{Bank} \right) \times EE$