FVA sceptics lose ground in valuation debate

The funding valuation adjustment, or FVA, is a bit like modern art. Everyone has a different take on it, stirring lengthy – and at times, heated – debates on how it should be interpreted. Some people rave about it, while some can't digest it at all, and others pretend to like it because of peer pressure. But despite this, there is a whole industry built around it.

Back in 2012, the argument was about whether FVA, which reflects the costs and benefits arising when uncollateralised derivatives are hedged with collateralised trades, should really exist. Dealers argued that it should, while academics angrily shook their heads.

For years, academics have argued that FVA breaks certain cherished financial principles that assume complete markets and perfect hedging. Under these assumptions, a perfectly hedged portfolio should grow at the risk-free rate. This rationale led them to conclude that derivatives should be valued by discounting cashflows at this risk-free rate. But dealers say markets are incomplete, because there is no liquid two-way borrowing and lending market – and as a result, derivatives should be valued using the bank's funding rate.

The fact that at least 29 major dealers have now accounted for the charge in their books should serve as evidence of which side is winning, but the reality is a bit more complicated.

Some banks cite peer pressure as the reason they chose to account for FVA in the first place. The numbers reported vary widely across the industry and bank disclosures on how they calculate the adjustment are sketchy at best. Added to this, a recent technical paper published on Risk.net showed that existing models overstated FVA by almost two times, sparking a huge debate as to whether current models need a revamp. Given these issues, it's not surprising that FVA is still on shaky ground.

Mathematically disproving the arguments of sceptical academics is perhaps a good way to start fixing FVA's fundamental problems. One paper published this month on Risk.net – The funding invariance principle – does exactly that. In the paper, Youssef Elouerkhaoui, the global head of credit quantitative analysis at Citi, shows that the risk-free rate – or any short rate used to discount the cashflows of a derivative – is irrelevant in the valuation of a derivative.

According to Elouerkhaoui, there are only two sources of funding one should consider for a derivative: the credit support annex rate, which is the rate earned on posted collateral, and the funding rate charged to the desk by treasury. Once all the individual cashflows of a trade are written down and added to the cashflows from collateral and treasury, he argues, the risk-free rate used to discount those cashflows ultimately cancels itself out – thereby making it irrelevant.

FVA's leading opponents – the University of Toronto's John Hull and Alan White – have argued the FVA of a portfolio, as typically calculated, is equal to the present value of the extra return required by lenders to compensate them for the cost of possible defaults by the dealer on its funding. This should be equal to the benefit to the dealer from possible defaults on its debt – also known as debit valuation adjustment 2 (DVA₂). Because the trading desk would benefit from DVA₂, it would not have to recover its funding cost separately.

To counter this argument, Elouerkhaoui uses existing accounting principles to define something called a fair-value option (FVO) debt CVA – part of US Financial Accounting Standard 159 that allows debt instruments to be reported at fair value. FVO debt CVA, which represents the benefits stemming from the deterioration of the dealer's own credit spread, is essentially the DVA₂ of a trade.

Take a bank that issued a bond at 400 basis points five years ago, but is able to issue similar debt today at 100bp. In principle, if that bank were taking an FVA adjustment on its books, it should be charging its trading desk at 400bp – the initial spread at which the bond was issued. But with FVO accounting, the bank can now charge 100bp, essentially marking the funding to today's market. That would reduce the bank's FVA, but wouldn't cancel it out to zero, as Hull and White have argued.

Elouerkhaoui's paper is not the first to have taken a stab at disproving traditional pricing constructs. In their previous work, respected quants Damiano Brigo, Andrea Pallavicini, Daniele Perini and Vladimir Piterbarg have all shown that the risk-free rate is essentially irrelevant to pricing. While past research has largely focused on the Black-Scholes framework to prove this, Elouerkhaoui uses a more general setting and is able to incorporate DVA, FVA, credit valuation adjustment and margin valuation adjustment.

The case for FVA – and for discarding standard models that rely too heavily on the risk-free rate – has only been getting stronger over the years. Now that some of the more fundamental questions have been answered, it's time to focus on another important issue that has received more scrutiny from dealers and regulators in the past year: getting the numbers right.