XVA stands for Valuation Adjustments, i.e. the valuation of the credit, funding and regulatory capital requirements embedded in derivative contracts. Traditional risk-neutral pricing assumes risk free discounting and neglects all these aspects, so adjustments need to be added to account for them. “Adjustment” does not mean it is minor, and XVA adjustments can be very significant.

## The Valuation adjustments

### CVA/DVA: Credit Risk

Unsecured portfolios represent the standard case for CVA as both counterparties are fully exposed to each other. CVA (Credit Value Adjustment) represents the expected cost of the default of the counterparty, while DVA (Debit Value Adjustment) represents the expected “benefit” of its own default, or more intuitively this is the CVA as seen from the other counterparty.

A derivative having a positive value in the future is at risk of this value never being paid by the counterparty in case it defaults. Thus, CVA can be seen as an option of strike 0 on the value of a portfolio. This is why it is so complex. One needs to model a whole portfolio (the netting set), which requires a multi-factor hybrid model as long as the portfolio is not trivial, and price some options on top of it.

DVA is the CVA as seen from the other side, so it’s computed the same way as CVA. But it remains counter intuitive as it involves recording a gain as the bank’s own credit risk deteriorates.

Non perfectly collateralised netting sets will potentially exhibit some CVA/DVA, as the counterparty exposure is reduced but not fully removed.

### FVA: Funding

FVA represents the expect cost of funding unsecured derivative transactions. For instance, a funding cost arises when a derivative has a positive market value. The purchase of this in-the-money position requires the bank to pay cash. This cash has to be funded at a rate which will be higher than the risk-free rate, thus effectively funding the position will have a cost.

### MVA: Initial Margin

While a perfectly collateralised netting set will have no CVA/DVA, new collateral agreements require each counterparty to post initial margin. This initial margin needs to be funded. The MVA represents the expected cost of funding the initial margin.

Initial margin was previously limited to central counterparties. The new regulations requires all new bilateral transactions to be included in netting sets posting initial margin, so that MVA has become a prominent valuation adjustment.

### KVA: Capital

Banks are required to hold capital reserves in order to survive large unexpected credit, market or operational risk losses. The introduction of Basel III has substantially increased the capital required by banks for holding derivative contracts. KVA captures the cost of this additional regulatory capital.

## Complexity

### A portfolio dependant measure…

The complexity is mainly due to the fact that XVA is a portfolio dependent measure. The XVA at a deal level is not relevant as a single deal can increase or reduce the exposure to a counterparty depending on the composition of the whole portfolio. Usually the relevant perimeter is the netting set, except for KVA market risk where it is the global position.

An XVA adjustment can be seen as a range of options (nonlinear function) of different maturities on the value of a portfolio, a quite exotic structure.

This requires a modelling of the whole portfolio with a multi-factor model, the number of factors outweighing what is usual for exotic products. For instance, a portfolio containing only interest rate products in 5 currencies will require at least 9 factors (5 currencies and 4 FX), more if one wants several factors per currency. On top of that, the number of flows to simulate will be very high.

Innovative technologies need to be set up in order to cope with the massive computational burden.

XVA is also transversal by nature, so any silo within an institution between asset classes will cause unsolvable problems.

### … requiring a central XVA desk

As netting sets can span multiple asset classes, the traditional organisation of a financial institutions with multiple business lines split by asset class, is no longer relevant. A central XVA desk has to be set up to risk manage globally the XVA.

The central XVA desk will typically charge the valuation adjustments to the other trading desks, so that each trading desk sees trades as if they were perfectly collateralized, the difference being managed by the XVA desk.

Whether the central XVA desk wants to actively risk manage its XVA or not is another story. Computing the XVA risks is itself even much more computationally intensive than XVA.