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Hello David! I have noticed that formula for both expected loss and CVA is the same. CVA is the present value of future exposure. Isn't expected loss the same thing? I am aware that EL is used for both credit risk and counterparty credit risk. So, why CVA if we can measure CCR with EL? Would be great if you could shine a light on the same.

David Harper CFA FRM

David Harper CFA FRM
Staff member
Hi @Sameera Yes, I agree with you, and I this it's easiest to understand CVA as an EL designed for the bilateral context. For example, as I wrote here https://www.bionicturtle.com/forum/threads/credit-var-vs-cva.9563 i.e.,
I would start with this: the credit value adjustment (CVA), because it assigns a price to counterparty risk, is essentially an estimate of expected (future) losses, while credit value at risk (CVaR) is an estimate of (future) potential unexpected losses (UL). At the risk of brutal and indefensible simplification :eek: : CVA --> EL and CVaR --> UL.

... and then mathematically here at https://www.bionicturtle.com/forum/...-value-adjustment-cva-gregory.7826/post-44152 i.e.,
CVA is the price of (credit) counterparty risk, so its (abstracted) formula is similar to expected loss (EL) = PD*EAD*LGD; i.e., CVA ~= PD(Δt)*EE(Δt) *LGD. Whereas EL is the price of default risk in a "unilateral" long bond position (by which I mean, the lender is funding the loan so the lender has unilateral exposure) to a bond, CVA is similarly the price of default risk for a bilateral derivative position. Standalone CVA simply refers to this credit risk price (ie, CVA) for a single trade or position. Both marginal and incremental CVA only have meaning when the position becomes a component in a larger "portfolio," where the portfolio is the netting-set of trades under a netting agreement. Netting allows for the "diversification benefit" which, in this context, is the ability to reduce the netting-set's total price of counterparty risk (aka, CVA).