XVA (CVA/FVA) Mechanics

XVA adjusts idealised prices for counterparty, funding, and capital effects along the exposure profile.

Explanation

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.

In practice, XVA couples pricing, risk, and treasury constraints into a consistent adjustment framework.

xvacvafvaexposurefunding

Interactive visualisation

XVA adjusts an idealised, risk-free price for counterparty and funding effects along the exposure profile. Here we use a stylised expected positive exposure (EPE) hump and show how hazard rate, LGD and funding spread turn that profile into CVA and FVA amounts.

Exposure scale (rough units, e.g. millions): 10.0Counterparty hazard rate λ (annual, %): 2.0%Loss given default (LGD, % of exposure): 40%Funding spread (s_F, annual, %): 1.0%

Numbers

λ ≈ 2.0% per year, LGD ≈ 40.0%

Funding spread s_F ≈ 1.0%

CVA ≈ 0.31 (loss from counterparty default)

FVA ≈ 0.39 (cost of funding exposure)

Base price 100.00 → XVA-adjusted ≈ 99.30

Interpretation

The blue curve shows how much you are exposed on average through time. CVA and FVA are just discounted integrals of that profile against credit and funding parameters. Increasing hazard or LGD raises the orange CVA block; increasing funding spread raises the green FVA block.

XVA is therefore not a separate “model world”: it is a systematic way of mapping an exposure profile into price adjustments that reflect counterparty quality and the cost of financing the trade and its collateral over its life.