XVA and Counterparty Risk

The XVA section adds counterparty and funding effects to an otherwise clean derivative value. CVA is the expected loss from counterparty default on positive exposure; FVA captures the funding cost of carrying an uncollateralized position. The exact decomposition depends on collateral, netting, and the institution's convention.

The calculation is path dependent: simulate or approximate future exposure, combine it with default probabilities and recovery, and discount the expected loss. Netting sets and collateral agreements can change the exposure more than a small shift in a market input.

The class notes use XVA to connect pricing and risk governance. A model output is meaningful only when the legal agreement and the exposure definition are the same ones used by the desk.