  An uncollateralized swap hedged back-to-back by a CCP swap is used to
introduce FVA. The open IR01 of FVA, however, is a sure sign of risk not being
fully hedged, a theoretical no-arbitrage pricing concern, and a bait to lure
market risk capital, a practical business concern. By dynamically trading the
CCP swap, with the liability-side counterparty provides counterparty exposure
hedge and swap funding, we find that the uncollateralized swap can be fully
replicated, leaving out no IR01 leakage. The fair value of the swap is obtained
by applying to swap's net cash flows a discount rate switching to
counterparty's bond curve if the swap is a local asset or one's own curve if a
liability, and the total valuation adjustment is the present value of cost of
funding the risk-free price discounted at the same switching rate. FVA is
redefined as a liquidity or funding basis component of total valuation
adjustment, coherent with CVA, the default risk component. A Longstaff-Schwartz
style least-square regression and simulation is introduced to compute the
recursive fair value and adjustments. A separately developed finite difference
scheme is used to test and find regression necessary to decouple the discount
rate switch. Preliminary results show the impact of counterparty risk to swap
hedge ratios, swap bid/ask spreads, and valuation adjustments, and considerable
errors of calculating CVA by discounting cash flow or potential future
exposure.
