A Simple Look at XVAs (CVA, DVA, FCA, KVA)

Abstract

Using a simple one-period model of XVAs (CVA, DVA, FCA, KVA) I derive some interesting results: 1) A change in the bank’s borrowing cost does not impact P&L because the change in trade value (through DVA, FCA) is offset by a change in the value of the bank’s debt. 2) CVA represents the cost of hedging counterparty credit risk, though has the same value regardless of whether counterparty credit risk is actually hedged. However, the decision of whether to hedge CVA affects FCA and KVA: -FCA (Funding Cost Adjustment) - Since hedging CVA means funding a CDS premium. -KVA (Capital Value Adjustment) - Since hedging CVA reduces the trade’s capital requirement. The effects in 2), FCA and KVA are offsetting, so we can’t say in the real world whether it will be economical for a bank to hedge CVA or not. The affect in 1) doesn’t translate exactly to the real world due to factors such as the different tenors of a bank’s funding requirements and actual borrowing and different accounting treatments for borrowing and trading.