How does bilateral CVA incorporate both parties' default risk, and what role does netting play in the calculation?

Bilateral CVA recognizes that both counterparties in a derivatives transaction face credit risk. While unilateral CVA only accounts for the counterparty's potential default (when you have positive exposure), bilateral CVA also considers what happens when your firm defaults while owing money to the counterparty.\n\nBilateral CVA Framework:\n\nBilateral CVA = CVA - DVA\n\nWhere:\n- CVA = Expected loss from counterparty default (when exposure is positive for you)\n- DVA = Expected gain from your own default (when exposure is negative for you -- you owe them)\n\n`mermaid\ngraph LR\n A[\"Your Firm\"] -->|\"Positive exposure
They owe you\"| B[\"Counterparty\"]\n B -->|\"Negative exposure
You owe them\"| A\n A -->|\"If they default
You lose = CVA\"| C[\"Credit Loss\"]\n B -->|\"If you default
You 'gain' = DVA\"| D[\"Credit Benefit\"]\n C --> E[\"Bilateral CVA
= CVA - DVA\"]\n D --> E\n`\n\nBilateral CVA with Netting:\n\nConsider Arkwright Financial with counterparty Blackstone Holdings. Under a single netting agreement:\n\n| Trade | Notional | MtM (Arkwright view) |\n|---|---|---|\n| 5Y interest rate swap | $200M | +$4.2M |\n| 7Y cross-currency swap | $150M | -$2.9M |\n| 3Y equity swap | $80M | +$1.1M |\n| Net | | +$2.4M |\n\nWithout netting, Arkwright's gross positive exposure = $4.2M + $1.1M = $5.3M\nWith netting, net positive exposure = max($2.4M, 0) = $2.4M\n\nNetting reduces the exposure base for CVA by more than half.\n\nFor DVA, Arkwright's negative exposure without netting = $2.9M.\nWith netting, DVA is calculated on the counterparty's positive exposure = max(-$2.4M, 0) = $0 (since net MtM is positive for Arkwright).\n\nNumerical Bilateral CVA:\n\nAssume simplified 1-year horizon:\n- Blackstone's default probability: 2.5%, LGD: 55%\n- Arkwright's default probability: 1.8%, LGD: 55%\n- Expected Positive Exposure (Arkwright perspective): $3.1M\n- Expected Negative Exposure (Arkwright perspective): $1.7M\n\nCVA = 0.55 x 0.025 x $3.1M = $42,625\nDVA = 0.55 x 0.018 x $1.7M = $16,830\n\nBilateral CVA = $42,625 - $16,830 = $25,795\n\nThe DVA Controversy:\n\nDVA implies your derivatives portfolio gains value when your own creditworthiness deteriorates -- a counterintuitive and controversial result. A firm nearing bankruptcy would report DVA gains, which is economically questionable. This controversy is why regulators disallow DVA in regulatory capital calculations despite its inclusion in accounting standards (IFRS 13).\n\nDive deeper into bilateral CVA in our FRM Part II materials.