A swap can lose value because its counterparty weakens even when every payment arrives on time. Pricing that deterioration requires the future exposure profile, the default curve and the contract's protection terms together.
The default-free value assumes every promised payment will be made. A risky counterparty may fail when the derivative is an asset to you. Credit valuation adjustment (CVA) deducts the discounted expected shortfall from that default-free price. A credit limit constrains how much risk you accept; CVA prices the risk you accept. Charging CVA does not make an excessive concentration acceptable.
Pricing is difficult because exposure changes with market prices, and default may occur precisely when exposure is high. Netting, collateral, recovery, close-out terms and default timing all affect the loss. A counterparty without liquid credit default swap (CDS) quotes also requires a defensible proxy credit curve. The selected proxy introduces basis risk, even when the calculation is accurate.
Use a positive number for a CVA cost throughout this lesson. Some sources report the same adjustment as a negative contribution to value.
Common mistakes
- Using cumulative PD in each interval. A 5% two-year cumulative PD does not mean 5% default probability in both years. Use survival differences or the supplied unconditional interval probabilities.
- Calling an upfront fraction a running spread. Example 1's 25.44 basis points of notional becomes a 13.39-basis-point running charge after dividing by the payment annuity.
- Calling every unilateral subtraction exact BCVA. First-default conditions remove losses occurring after the other party already defaulted. Use the stated close-out convention and approximation.
Bottom line
- Positive CVA is a cost deducted from clean value; interval default probabilities must match the exposure dates.
- A running adjustment divides its upfront amount by the actual notional-weighted fee annuity.
- DVA uses own-default risk and negative exposure; exact bilateral valuation accounts for first default and close-out.
- Netting acts path by path; incremental CVA prices an addition, while marginal CVA allocates the current total.
Exam shortcut
Write the perspective, sign convention, probability measure and exposure units before calculating. For a stress loss, identify whether the question wants a stressed level, an increase from baseline or a loss conditional on default. For a quoted spread, locate its payment annuity before dividing. Continue with structured credit and securitization to apply loss allocation to pools and tranches.
The full lesson (about 4,550 words, 30 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
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