XVA 3 - DVA, the forgotten XVA
While CVA and FVA (the subjects of two previous blogs) are widely used in pricing for derivatives, DVA has largely fallen from use in banks. DVA may seem to be abandoned, but it is still in general use for some applications.
For example, DVA is still widely used in accounting for derivatives (fair value) for buy-side firms. It is a necessary part of the reporting requirements and is included in the Fair Value reporting for derivatives.
This blog looks at DVA, why it was used previously by banks, why it was discontinued and why it is still used by the buy-side.
It may be the forgotten XVA for banks but it remains important and this blog looks at how it is calculated.
The history of DVA with banks
From the early 2000’s many banks routinely reported CVA and DVA adjustments to their derivative valuations.
This was widely seen as ‘best practice’ because it created a degree of symmetry - your CVA is my DVA and vice versa. When you think about it, for a bank, the negative and positive exposures to eachother when combined with the same CDS inputs would create equal and offsetting P&L calculations for CVA and DVA. It provided a very neat way to balance books and valuations between counterparties.
However, DVA (as you will see below) is really a calculation of the credit exposure of a counterparty on your bank. If you were to default, then presumably you would not pay the counterparty and the positive DVA would effectively offset the payment you would now not make. This all sounds perfectly reasonable, but in practice this may not be as clean as it appears in case of default. In practice, the process of resolution (see the Lehmann example from 2008) is complex and DVA may not accurately the final settlements.
Also, as your credit quality deteriorates, DVA increases and adds positive valuation to the derivatives books. Predictably, this did not sit well with auditors to the banks, and it was discontinued.
A great example is JP Morgan who posted a huge positive DVA valuation adjustment in 2011 (around $1.1 billion) and eventually recorded a $1.5 billion loss as DVA was removed in 2014.
I expect the whiplash was part of the reason many banks removed DVA form valuations at similar times and simply too the loss.
DVA Calculations
DVA is calculated in a very similar way to CVA and from the same simulations.
DVA = -LGD * ∑ (ENE * PDs)
LGD = Loss given default (assumed to be 60%)
ENE = Discounted Expected Negative Exposure where only negative exposures are included. Note CVA uses EPE which are the positive exposures.
PDs = Probability of default of yourself (market input)
The derivative is divided into a number of time steps and the ENE is calculated at each step in a similar way to the EPE.
Similarly, PDs is calculated in the same way as PDc for CVA using your CDS curve rather than the counterparty CDS curve as the input.
Expected Negative Exposure (ENE)
The ENE is used because the only time a bank has credit exposure to the counterparty is when the counterparty trade is ‘out of the money’ for the bank, i.e., when the bank owes money to the counterparty based of the forward valuations. For example:
an at the money interest rate swap has some time in and some time out of the money if the yield curve is not flat;
an interest rate swap with very large positive PV for the bank will have most time in the money; and
an interest rate swap with very large negative PV for the bank will have very little time in the money.
The ENE (from the bank’s perspective) will be impacted by the current PV of the derivative as well as the forward PVs.
The diagram to the left shows the Monte Carlo simulation for a ‘bought’ position in AUD/USD with the EPE and ENE marked on the right.
At the money is the blue line and the paths below that line represent the ENE, i.e., where the bank of out of the money.
As you can see, the same simulation is used to calculate the EPE and ENE but different paths are chosen for the CVA and DVA calculations.
Summary of DVA
DVA represents the expected cost of the credit exposure of the counterparty to a bank.
Banks do not include the DVA in pricing for derivatives.
DVA is calculated in a veery similar way to CVA but using the ENE rather than the EPE and a CDS curve of the bank.
Like CVA, best practice for DVA calculations is a full monte carlo simulation.
DVA is dynamic: it changes over time as settlements occur, and market PV moves.
DVA is routinely included in the buy-side FAIR Value reporting of derivatives.
Implications for the buy-side
This has some serious implications for the buy-side.
DVA is always a positive in a buy-side firm’s derivative Fair Value.
DVA is not replicated by banks so will not form part of their pricing and/or restructuring pricing.
FVA is used for derivative pricing but is not included in the buy-side Fair Value reporting.