CVA schematic
CVA approx sum_t DF(0,t) LGD EE(t) Delta PD(t)CVA aggregates discounted expected loss across future default intervals.
Research & Systems
XVA (CVA/FVA) Mechanics
XVA adjusts idealised prices for counterparty, funding, and capital effects along the exposure profile.
Mental model
XVA adjusts idealised derivative value for the financing, counterparty, and capital realities of exposure.
CVA is the expected discounted loss from counterparty default, integrating exposure, LGD, and default intensity.
FVA captures the cost or benefit of funding collateral and hedges over the life of a trade.
Explore the mechanism
How do exposure through time, counterparty default, collateral, and funding alter an otherwise idealized derivative value?
CVA weights future net exposure by marginal default probability and loss given default. FVA separately weights funding requirement by funding spread through time.
Gross exposureNet after collateral
0.5y
1.0y
1.5y
2.0y
2.5y
3.0y
3.5y
4.0y
4.5y
5.0y
CVA 0.302default-weighted lossFVA 0.287funding-weighted requirementTotal adjustment 0.590compact educational sum
With 25% collateral, the blue net-exposure line sits below gross exposure. Hazard and recovery change CVA; funding spread changes FVA. Collateral affects both, but through different weighted profiles.
UNDERSTAND
What to notice
In practice, XVA couples pricing, risk, and treasury constraints into a consistent adjustment framework.
The quantitative structure
Notation
EE(t)- expected positive exposure at time t
PD(t)- counterparty default probability term structure
LGD- loss given default
DF(0,t)- discount factor
This model assumes
- Exposure, default, recovery, collateral, and discounting conventions are internally consistent.
- Dependencies such as wrong-way risk are either modeled or explicitly excluded.
Where it appears
- pricing counterparty credit risk
- managing collateral and funding costs
- measuring CVA sensitivities and capital
Where the intuition breaks
What this view leaves out
- XVA components depend on conventions, netting, collateral, funding policy, wrong-way risk, and model choices; naive addition can double-count effects.
Common mistakes
“XVA is a single universal adjustment quoted identically by every institution.”
Not quite.Components depend on institution-specific funding, agreements, accounting, and modeling choices.
Where this concept sits
Follow the strongest prerequisites, applications, extensions, and contrasts.
Connections for XVA (CVA/FVA) Mechanics
XVA (CVA/FVA) MechanicsYOU ARE HERE
UsesCredit Intensity Models and Default CorrelationCredit intensities and dependence assumptions feed counterparty default and exposure-adjustment calculations.
ExtendsMark-to-MarketXVA adjusts clean mark-to-market value for counterparty, funding and related effects.
UsesMonte Carlo PricingExposure profiles for XVA are often generated by simulating future market states and portfolio values.
UsesYield Curve BootstrappingXVA calculations require term structures for discounting, funding and often credit-related quantities.
Related toLiquidity vs Solvency RiskFunding valuation adjustments connect derivative valuation with funding and liquidity considerations.
Uses · Credit Intensity Models and Default Correlation
Credit intensities and dependence assumptions feed counterparty default and exposure-adjustment calculations.
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