XVA 2 - Funding Valuation Adjustment (FVA)

Pricing and Market Dyn
Written By John Feeney

This blog moves on from CVA to FVA and looks at the importance of this critical XVA in pricing derivatives.

As with CVA, FVA has an interesting history in pricing of derivatives.

Once upon a time, derivatives were believed to be ‘off balance sheet’ and relatively neutral for funding requirements. The settlements in or out were netted (e.g., in a swap the pay and receive sides were netted) so large cashflows would not happen.

Then derivative books grew in size, maturity and the products they supported. Some of these products such as cross-currency swaps could create significant funding requirements so derivative books were challenged on the off-balance sheet assumption.

FVA is the quantitative calculation of the funding and on-balance sheet implications of derivative books.

Now derivatives are very much on-balance sheet

My preferred approach is to think about a derivatives book in classic finding terms such as asset and liability.

Derivative books are mark-to-market in banks and the Net Present Value (NPV) is calculated daily. Typically, the books have zero value at the beginning of each day:

  • A positive NPV is offset by an equal and opposite, negative cash position (i.e., it looks like a loan or asset).

  • A negative NPV is offset by an equal and opposite, positive cash position (i.e., it looks like a borrowing or liability).

  • The cash position needs to be funded or invested.

  • Many banks apply a funding spread to borrow or lend the cash to the offsetting position in the derivative book maturity.

  • The funding spread is set internally in banks and can differ in size and complexity.

If the funding spread is positive (and it typically is positive) then the derivative book earns the spread on a liability and pays the spread on an asset. This looks just like a loan book except a derivative book calculates the NPV of that spread and it is a day 1 cost or benefit to the bank.

The NPV of the funding spread is FVA.

But unlike CVA, the FVA can be positive or negative for the bank and will be reflected in the price shown to a client.

Calculations

FVA is calculated using similar inputs to CVA:

  FVA = ∑ (EE * FSs)

 EE = Expected exposure, sum of EPE (expected positive exposure, as per CVA) and ENE (expected negative exposure)

  FSs = Bank funding spread

The calculation is done in discreet time steps so that the EE and FSs are specific to that time step. The individual time step calculations are discounted and summed over the entire trade until maturity.

The EE will vary in the future based on the forward value of the derivatives. Better practice is to model the EE and many banks use models such as monte calrlo to achieve this outcome.

But, unlike CVA, no LGD is used in the calculation.

The funding spread between ti-1 and ti is:

 FSs(i-1,i) = exp(-Fi-1 * ti-1) - exp(-Fi * ti)

where Fi = bank’s funding spread at time i (i.e., cost of funds over a base curve such as SOFR)

I also note that some banks also apply a spread to the funding spread to allow for the difference between the borrowing and lending rates internally. This is not a universal feature of FVA pricing but it can be used by some banks.

Collateral implications

If the 2 parties collateralise the derivative between them, then FVA is not required.

The collateral (variation margin) offsets NPV cash position and the return of the collateral aligned to the settlements of the derivative in the future.

But collateral comes with its own XVAs - more on this in later blogs.

Summary of FVA

FVA represents the on-balance sheet implications for banks

  • FVA is calculated from the EE and the bank’s internal funding spread.

  • EE is typically calculated across the life of the derivative using models such as monte carlo.

  • FVA can be positive or negative unlike CVA which is always a cost to the bank.

Implications for the buy-side

This has some serious implications for the buy-side.

  • FVA can be a charge or benefit to the client.

  • Buy-side needs to be aware of the pricing and that banks do differ in their methodologies and inputs, particularly the funding spread.

  • This means they will have different prices - so it pays to ask specifically for the FVA charge or benefit.

  • PV is important and trades that are significantly in or out of the money will attract very different FVA charges.

  • If you use collateral, this will largely remove FVA but will be replaced with other XVAs

Recommendations

As I wrote for CVA, I always approach XVAs carefully while recognising different banks can use different methodologies and inputs,

This means they will have different prices, and it is important to understand their approach. Since I have been assisting buy-side clients with pricing and trade execution, I have been able to observe the way many banks price FVA. But I always calculate the FVA before approaching the banks so I can base-line the expected responses.

I suggest buy-side clients:

  • Plan trade execution and calculate the FVA before asking for pricing from banks - you may need some assistance in this calculation.

  • Understand why banks are pricing FVA in a particular way.

  • Negotiate and ask questions.

  • Be confident and get some independent assistance if required.

John Feeney
Next

XVA 1 - Credit Valuation Adjustment (CVA)