Counterparty Risk and CVA

An interest-rate swap has zero value at inception, but it isn't risk-free — if it moves in your favor and your counterparty then goes bankrupt, you can lose the gain you were owed. That risk — that the other side of a derivative fails to pay — is counterparty credit risk, and its price tag is the credit valuation adjustment (CVA): how much a bank shaves off a trade's value to account for the chance the counterparty defaults while still owing money.

What actually gets priced

CVA depends on three things multiplied together at each point in time: how much you'd lose if the counterparty defaulted right then (exposure), how likely the counterparty is to default around that time, and how much of the loss you'd actually recover.

$$\text{CVA} \approx \sum_t \text{EE}(t) \times \text{PD}(t) \times (1 - \text{Recovery})$$

In words: at each future date $t$, take the expected positive exposure — how much you're owed on average, but only counting scenarios where you're owed anything at all — multiply by the probability of default around that date, multiply by the fraction you wouldn't get back, and add it all up across the life of the trade.

The exposure term is the subtle part. A swap's value swings both positive and negative as rates move, so exposure is not the swap's current mark — it's the expected value of only the upside scenarios, since a downside scenario (you owe them) creates no loss if they default.

Worked example

A bank has a 5-year swap with a hedge fund counterparty. Modeling shows an average expected positive exposure of $4 million over the life of the trade, the counterparty's default probability over that period is 3%, and recovery on unsecured claims in default is typically 40%.

1. Loss given default. $1 - 0.40 = 0.60$, so 60 cents on the dollar is lost if default happens.
2. CVA. $4,000,000 multiplied by $0.03 \times 0.60 = 0.018$ gives $72,000.
3. Interpretation. The bank should book this swap roughly $72,000 cheaper than its "clean" market value, purely to reflect that the hedge fund might not pay if it's ever in the money to the bank.

What this means in practice

Banks add CVA desks precisely because this charge moves independently of the underlying trade — a swap can sit flat while CVA swings hard just because the counterparty's credit spread widened. That's why CVA is hedged separately, often with CDS on the counterparty itself, and why post-2008 capital rules (CVA capital charges under Basel III) made this desk's risk management a regulatory requirement, not just good practice.