Simple example of a funding valuation adjustment? To discuss Funding Valuation Adjustments (FVA) it is first necessary to describe a situation in which such an adjustment would be needed In here we will take as an example collateral mismatches, which is a common case For a conceptual treatment of FVA and collateral mismatches refer to Ruiz (2013) We borrow the modified Black-Scholes framework of Piterbarg (2010) We assume we have sold a
2 Ways to Define Calculate FVA? - Same or Different? (Simple XVA . . . 3 I've got a very simple question on 2 different ways of defining or calculating the FVA of an uncollateralized swap One definition I've often seen is that the FVA is the difference in the net present value of the swap discounted using the risk free rate (e g , OIS) and that of the same swap discounted using the bank's funding rate (e g , LIBOR)
What is meant by the funding cost of a derivative? FVA attempts to capture the cost of funding uncollateralised OTC derivatives Similarly, a funding cost arises for the bank when a derivative has a positive market value The purchase of an ‘in the money’ or asset position derivative requires the bank to pay cash
Funding Valuation Adjustment (FVA) - understanding issues The mathematics is quite nice actually, and you find that the doubly survival - contingent FVA term + the bank first to default term collapse to a symmetric bank defaults first term Again, if get some time later will write out the relevant time integrals as an answer
Is Piterbargs FVA equation generally applicable My understanding is that the idea of applying a FVA, which reflects the cost of hedging any general derivative on a cleared market, is applicable to any derivative that is not perfectly collateralised The source of this question is that I've seen this similar (if not equivalent) equation to Piterbarg's used to calculate FVA for swaps:
interest rate swap - IRS with early termination provision . . . The reason being that the swap is guaranteed to exist only for a certain amount of time hence it typically lowers the calculation of CVA FVA charges From the IRS perspective they are valued as normal, and hedged as normal