CVA Tail Risk and Portfolio Netting for Derivatives

Book: Financial Risk Management: Applications in Market, Credit, Asset and Liability Management and Firmwide Risk Authors: Jimmy Skoglund & Wei Chen ISBN: 978-1-119-13551-7

Pricing CVA is one problem. Managing CVA risk across a portfolio is another. This section covers the full CVA distribution, tail risks, and multi-trade counterparty portfolios.

The CVA distribution

The exposure simulation that produces CVA also produces a distribution of CVA values across scenarios. You can compute VaR and CVaR on that distribution, not just the expected CVA charge.

Basel III’s CVA capital charge uses the conditional distribution of CVA given current exposure, treating exposure as fixed. That captures credit spread volatility but not full market-and-credit joint risk.

Tail risk example

Skoglund and Chen run 10-year payer and receiver swaps under three CVA distributions: default risk only, market risk only, and both with 80% wrong-way correlation.

For an ATM 10-year payer swap, the 99% CVA VaR from default risk alone is about 2% of notional. The current CVA charge is only about 1%. Market risk alone produces an even higher tail charge.

When both risks combine with wrong-way correlation, the 99% VaR roughly doubles versus either alone. Wrong-way risk inflates tails more than it inflates expected CVA. Tail CVA risk often stays unhedged and must be capitalized.

Portfolio netting

Without a netting agreement, each trade’s exposure is max(value, 0) and you sum them. With an ISDA netting agreement, portfolio exposure is max(sum of all trade values, 0).

Example: four swaps. Sum of individual CVAs is about 26,449. Netted portfolio CVA is about 3,259. Netting cuts CVA by a factor of roughly 8.

Netting only helps when offsetting trades exist in the same netting set. Multiple netting sets per counterparty aggregate in two steps: net within each set, then sum across sets. Collateral agreements attach to netting sets.

Euler decomposition

How do you assign portfolio CVA back to individual trades? Euler allocation, same technique used for market VaR and portfolio credit risk.

For expected exposure, the marginal contribution of trade m is the average value of trade m on paths where netted portfolio exposure is positive. Contributions sum to total EE.

This supports post-trade marginal analysis, pre-trade incremental analysis, and capital allocation across desks.

New trade impact

Before booking a deal, the desk checks incremental CVA and incremental peak exposure against counterparty limits. The CVA desk’s incremental quote is the pre-deal decision tool. Historical CVA premiums are tracked so if a trade is cancelled later, the desk can settle the P&L impact with the trading desk fairly.

Post-deal, marginal contributions feed limit reports and help decide which trades to novate, compress, or hedge with CDS.

Collateral in portfolio decomposition

When CSA applies to a netting set, collateralized exposure replaces raw exposure in the aggregation formulas. Euler decomposition still works but conditions on positive collateralized portfolio exposure instead of positive raw sum. This matters for desks that see near-zero CVA on collateralized books but still need to understand which trades drive margin calls.

Peak exposure and wrong-way CVA allocation

Peak exposure contributions use quantile-based conditioning rather than mean conditioning. Wrong-way CVA portfolio numbers require the full path-by-path engine. You cannot decompose wrong-way CVA with the simple independence formula. In practice, desks often report independent CVA contributions daily and reserve wrong-way adjustments for weekly or monthly runs.

My take

Netting is the first line of defense for any multi-trade counterparty relationship. Without an ISDA in place, you are overstating risk by a lot.

Expected CVA is what you charge. CVA VaR is what can go wrong on your hedge book. Basel III only capitalizes credit spread vol on CVA, but you need to understand market-driven tail risk too.

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