The cost of funding the hedge
To recap, the simplest and most common circumstance when FVA arises is when a bank has an unsecured trade with a counterparty and hedges it with a secured trade – for example with a CCP. In this case if the value of the trade is positive, the value of the hedge is negative. To cover the margin call the bank has to borrow cash at its funding rate of Libor+s where ‘s’ is its funding spread. The trade and associated funding terminates if either the bank or counterparty defaults. FVA is the expected value of the funding cost. It can be expressed as the expectation of the bank’s funding spread applied to a positive PV (discounted to today) until the deals maturity or early termination due to either bank or counterparty default.
There is still industry discussion how best to calculate FVA. However, an even bigger debate is centered on the questions: assume that banks know FVA, how should they handle it?
FVA: a hybrid of CVA and DVA
FVA is a hybrid of CVA and DVA. Like CVA, FVA depends on positive exposure and is a cost, i.e. has negative value. FVA is also proportional to a bank’s “own” spread (thus, default probability) like DVA. The difference between FVA and DVA is that CVA and DVA have symmetrical characteristics – a bank’s CVA is its counterparty’s DVA and vice versa, which allows both parties of the trade to agree on bilateral CVA (CVA-DVA). However, if we assume that the bank borrows at Libor+s but lends at Libor, FVA has no symmetrical part.
To price, or not to price?
There is still industry discussion on how best to calculate FVA. However, an even bigger debate is centered on the questions: assuming that banks know FVA, how should they handle it? Should FVA be a part of the price, as in the case of CVA and DVA? Alternatively, should it be part of the cost attributed to a particular trade? In other words, can traders pass this cost to the counterparty, or should it be absorbed by the bank (and charged to the desk)? If it is included in price, how do you convince the counterparty to accept the cost arising from the bank’s funding, and furthermore will it eventually lead to “natural selection” when banks with lower spreads win all the business?
Probably the biggest difference between FVA and other costs of incompleteness is that FVA is easier to quantify, at least for banks that have CVA systems in place.
Quantifi’s view: Markets are incomplete and so it’s a cost
Quantifi’s long-standing view is that FVA is not part of risk-neutral pricing but is a cost arising from market incompleteness. While risk-neutral pricing is derived under the assumption that both lending and borrowing are executed at risk-neutral rate, i.e. Libor, in reality borrowing is done at Libor+s, although before the financial crisis this difference was relatively small and was typically ignored. In this sense, FVA is similar to other signs of market incompleteness like price jumps or hedging costs.
Probably the biggest difference between FVA and other costs of incompleteness is that FVA is easier to quantify, at least for banks that have CVA systems in place. We believe that the market practice of covering this cost, by widening bid-offer spreads, will continue. However, banks will not be able to pass the whole cost on to their counterparties, and the remaining cost should be absorbed by the bank.
In any case, it is imperative to have a marginal profitability calculator which compares trade P&L (quoted price after subtraction of risk-neutral price and bilateral CVA) with FVA and other incurred costs, including regulatory capital charges. Only after this analysis, can the decision to execute any particular trade be done.