Funding Valuation Adjustment (FVA), Part 1: A Primer

March 20, 2014

The implementation of new regulations including Dodd-Frank, MiFID II, EMIR and Basel III is significantly increasing the cost of capital and forcing banks to re-evaluate the economics of their OTC trading businesses. McKinsey in its paper (2012) estimates that without mitigation the average Return on Equity (ROE) of the flow rates business will go from 19% to 8% post regulation, while ROE in structured rates will drop from 15% to 4%.

 

Understanding trade profitability becomes critical with banks now pricing all the components of a trade including the model value using the appropriate discounting curve, the credit valuation adjustment (CVA), the Cost of Regulatory Capital (CRC) and most recently the Funding Valuation Adjustment (FVA).

Accurately pricing CVA, CRC and FVA for a single trade requires taking into account all trades done with that counterparty, along with the collateral posted or received as part of any CSA. This presents new challenges for OTC businesses that have traditionally been siloed within banks. This challenge has driven a trend towards central measurement and management of these components by CVA desks with various strategies for allocating the P/L and risk of a trade between each trading desk and the CVA desk.

 

Funding Valuation Adjustment

The FVA is the latest significant innovation in measuring trade profitability and captures the impact of funding and liquidity on the cost of a trade. This cost depends on the nature of the CSA (for example is the trade collateralised, uncollateralised, or one-way) and the net collateral posted or received. To understand FVA we’ll look at both collateralised and uncollateralised swaps.

 


 

'This challenge has driven a trend towards central measurement and management
of  these components by CVA desks with various strategies for allocating the P/L and
risk of a trade between each trading desk and the CVA desk.'

 


 

Collateralised swaps

Consider a single collateralised swap between two counterparties Bank A and Bank B. Under terms of the CSA, as the market value of the swap changes, collateral is posted or is received. If the mark to market of the swap is negative under terms of the CSA, the bank must borrow funds to post as collateral. These funds will be borrowed at the bank’s unsecured borrowing rate. The collateral posted will earn an interest rate specified by the CSA, which will typically be the relevant OIS rate such as Fed funds or Eonia. If the mark to market of the swap is positive the bank will receive collateral from its counterparty, with the CSA rate paid to the counterparty.

The asymmetric nature of this cost of collateral adds additional costs to transacting the swap. The size of this cost relates to the difference between the bank’s unsecured borrowing rate and the CSA rate. In this sense the FVA is related to the DVA which is a reflection of the bank’s own likelihood of default.

 

Portfolio FVA

The above example for a single swap is clear but unrealistic. Typically there will be a range of trades across different asset classes. If we consider the case of a portfolio of swaps traded between two counterparties under a single CSA (or netting agreement), it can be seen that the cost of funding is based on the net mark to market for all swaps with that counterparty. Analogous to CVA, accurately calculating the effect of this asymmetrical funding cost or FVA requires taking into account all OTC trades with a given counterparty along with the terms of the CSA.
 

 

Pricing versus profitability

From the single swap example above, it can be seen that the two counterparties will not agree on a price if funding costs differ - even if both share similar counterparty risk (and CVA). FVA is more appropriate in the context of measuring the profitability of a trade rather than as part of a mark to market calculation.

Depending on the counterparty and type of trade, banks may take the approach of charging none or part of the FVA but many counterparties regard this cost as not theirs to bear.

 

Uncollateralised swaps

Next consider a single uncollateralised swap between a bank and a client, hedged with an offsetting trade with a central clearing counterparty (CCP). For the uncollateralised swap, no collateral is posted or received. If the swap is hedged with a counterparty where collateral is posted with a CCP, the cost of the hedge will include the FVA. It may be natural for the bank to allocate this cost to the client’s swap.

 

FVA valuation and correlation dependencies

Above we considered the case where a bank has an uncollateralised trade with a client and hedges with a CCP. In this case, if the PV of the trade is positive, the PV of the hedge will be negative, and to cover the margin/collateral call the bank has to borrow cash at its funding rate Libor + s where ‘s’ is a funding spread. The trade and therefore funding terminates if either the bank or counterparty defaults.

The value of the FVA is the expected funding cost over the life of the swap. More formally, it can be expressed as the expectation of the bank’s funding spread st applied to the expected positive PV (discounted to today) until the deal maturity, or early termination due to a bank or counterparty default.

When the trade PV is negative, though the hedging trade (via collateral calls) is generating cash which can be invested by the bank, it earns only the risk-free (CSA rate) return. This demonstrates the asymmetry which leads to higher cost for banks which have lower credit. As a result, such banks face a competitive disadvantage with lower trade profitability at the same price.

 

FVA as a hybrid

It can be seen that the FVA is a kind of hybrid of CVA and DVA. It is calculated based on a product of positive exposure (like CVA) but with bank default probabilities (like DVA). Notice also that because the PV under the integral in the expression for DVA is negative, its value is positive, but CVA and FVA are negative.

FVA can be reinterpreted as the expected loss which the funding company would incur if the bank defaults. This will only happen when the value of the hedge trade is positive for the funding company, and thus negative for the bank, therefore the original trade has a positive value to the bank. Consequently the bank’s FVA is a CVA from the point of view of the funding company. An important detail is that there is no symmetric positive offset like DVA and as a result the funding company charges the whole FVA to the bank.

The formula above is not the most general, in the sense that it doesn’t take into account the dependencies between each of the two credits (bank and counterparty) and the PV of the trade and between the two credits themselves. Note that the first type of dependency is wrong-way risk and it is characterised by wrong-way correlation. The second type is characterised by a type of first-to-default copula correlation.

For example, if the bank spread is lower than the counterparty spread and correlation between their defaults approaches 100%, both DVA and FVA are close to 0, but CVA remains relatively large. On another hand, wrong-way correlation between the trade PV and the bank’s likelihood of default will decrease DVA, increase FVA (in absolute value) but will leave CVA unchanged. In a similar fashion to CVA, modelling wrong-way risk is critical to accurately calculating the FVA.

 

Challenges

Calculating FVA presents significant modelling, organisational, and infrastructure challenges. Many of these challenges are shared with CVA so FVA provides a natural extension for CVA processes and systems.

 


 

'Analogous to CVA, accurately calculating the effect of this
asymmetrical funding cost or FVA requires taking into account all OTC
trades with a given counterparty along with the terms of the CSA.'

 


 

Organisation

FVA is one measure included in trade profitability. The allocation and management of this component presents significant organisational challenges. Banks adapt with several common alternate structures depending on the nature of their business and their size. Some more common alternative structures include:

  • FVA P/L and risk allocated and managed by a central CVA desk
  • FVA P/L and risk allocated and managed individually by desks with central oversight and infrastructure
  • FVA P/L and risk allocated and managed by each desk on an ad-hoc basis

 

Infrastructure

FVA, like CVA, presents significant infrastructure challenges. All trades with a given counterparty need to be valued from both a market perspective and a credit perspective. All of a banks OTC trades need to be combined along with market data, credit data, legal data and collateral.

 

Modeling

The concepts and motivations behind FVA are straightforward but there remains confusion and differences about its application and how it relates to other components of OTC valuation including DVA, DVA and CSA discounting. This is particularly the case when looking at the various CSA structures. These differences, along with the existence of alternate approaches and levels of sophistication for modelling wrong-way risk, result in differences in valuing FVA. When FVA is taken in the context of trade profitability, these differences are not a significant issue and as modelling becomes more sophisticated are likely to converge.

Modeling wrong-way risk is one of the more significant challenges and is one area of recent evolution. A related area of focus is incorporating the possibility of significant market shifts on the event of default. An example is a Lehman event where the default of a significant market participant would be expected to be accompanied by significant market shifts. More generally the possibility of extreme market events like Lehman or the possibility of a country exiting the Euro are increasingly being incorporated into modelling frameworks.

 

Conclusion

The cost of funding has become a significant topic for financial institutions and is regarded as a key component in analysing the exposures and profitability of a trade.

FVA is the latest market innovation that has rapidly become the standard for measuring funding cost. It is part of a triad of valuation adjustments (CVA, DVA, and FVA) which have to be taken into account when profitability of a trade is estimated. Unlike CVA, FVA is a cost which generally cannot be passed on to the counterparty and knowing it is imperative for successful management of the trading book. In addition, the value of the FVA charge is proportional to the funding cost of the bank, therefore banks with higher funding spread (i.e. worse credit) suffer lower profitability at the same trade price and risk becoming less competitive. Like CVA, valuation of FVA should take into account all kinds of dependencies: between bank credit and trade PV, between counterparty credit and trade PV, and between credits themselves. Ignoring these dependencies can lead to significant mispricing of FVA, and thus trade profitability.

The introduction of FVA is one further step towards a significant restructuring of the way OTC businesses are managed. These changes are having a profound effect on the organisational structure, analytics, and risk management systems of OTC businesses - a trend that will continue as more banks adapt to the new market reality.

Part 2 & 3

Funding Valuation Adjustment (FVA), Part 2: The FVA Debate
Funding Valuation Adjustment (FVA), Part 3: JPMorgan and FVA; Next stop XVA

Recommended Whitepapers

A First View on the New CVA Risk Capital Charge
Should Banks Charge for FVA?
IFRS13 - Accounting for CVA and DVA
CVA, DVA and Hedging Earnings Volatility