  This article presents FVA and CVA of a bilateral derivative in a coherent
manner, based on recent developments in fair value accounting and ISDA
standards. We argue that a derivative liability, after primary risk factors
being hedged, resembles in economics an issued variable funding note, and
should be priced at the market rate of the issuer's debt. For the purpose of
determining the fair value, the party on the liability side is economically
neutral to make a deposit to the other party, which earns his current debt rate
and effectively provides funding and hedging for the party holding the
derivative asset. The newly derived partial differential equation for an option
discounts the derivative's receivable part with counterparty's curve and
payable part with own financing curve. The price difference from the
counterparty risk free price, or total counterparty risk adjustment, is
precisely defined by discounting the product of the risk free price and the
credit spread at the local liability curve. Subsequently the adjustment can be
broken into a default risk component -- CVA and a funding component -- FVA,
consistent with a simple note's fair value treatment and in accordance with the
usual understanding of a bond's credit spread consisting of a CDS spread and a
basis. As for FVA, we define a cost -- credit funding adjustment (CFA) and a
benefit -- debit funding adjustment (DFA), in parallel to CVA and DVA and
attributed to counterparty's and own funding basis. This resolves a number of
outstanding FVA debate issues, such as double counting, violation of the law of
one price, misuse of cash flow discounting, and controversial hedging of own
default risk. It also allows an integrated implementation strategy and reuse of
existing CVA infrastructure.
