In the previous article in the series, we explained how the financial crisis of 2008 led to significant reform in derivative pricing, with adjustments relating to discounting, funding and credit growing in importance. We also took a first look at Credit Valuation Adjustments (CVA), which reflect the likelihood of counterparty default in derivative contracts and portfolios. We outlined why CVA makes the comparison of the "true" fair value of derivatives pricing on multidealer platforms difficult. Finally we introduced Credit Default Swaps (CDS) as traded instruments to hedge against default risk, and therefore as a market observable price for counterparty risk. The important question, though, is how does this translate into pricing impact?
The components of CVA
There are several important components forming the calculation of CVA. The first is the Probability of Default (PD) of the counterparty; this measures the likelihood of a default event. The second is the Loss Given Default (LGD) of the counterparty; this measures the proportion of the obligation owed by the counterparty that would not be expected to be recovered in the event of default. The third is the Expected Positive Exposure (EPE) of the trade; this measures the potential size of the obligation owed by the derivative counterparty.
Calculating Probability of Default (PD)
The probability of default represents the likelihood of a counterparty being unable to meet its obligations. One must consider, however, that the probability of default can be different depending on the time horizon being analysed. This is important because projected counterparty exposure might change over different time periods, and thus assigning the correct probability of default to the correct exposure is necessary. In particular, a term structure of default probabilities is required in order to calculate CVA.
One approach to calculating default probabilities is using CDS. The CDS market provides a market price of counterparty risk that can be observed for different contract tenors. Typically, there are traded CDS for large bank counterparties available in various tenors from 6m to 10y, allowing a term structure of default probabilities to be implied.
Considering Loss Given Default (LGD)
When a counterparty defaults, the loss to creditors is not necessarily the full exposure as some portion might be recovered from the defaulting counterparty. The size of the recovered exposure relative to the total exposure is referred to as the Recovery Rate. The balance is the amount expected to be lost in case of default, and this is referred to as the Loss Given Default (LGD). As CDS contracts only compensate protection buyers for the LGD rather than the notional exposure of the CDS contract, this is an important factor when interpreting the CDS.
Calculating Expected Positive Exposure (EPE)
The exposure to a derivatives counterparty can vary significantly over the life of a transaction, with the nature of the derivative product being an important factor in understanding how much exposure is potentially at risk should the counterparty default. Therefore, it is those exposures that hold a positive mark-to-market (MTM) that are relevant (that is, where the derivative counterparty has an obligation to the corporate at the time of default). It is for this reason that for CVA the expected positive exposure needs to be calculated. It can be thought of as a probability weighted average of all possible derivative valuations at a point in time, where negative valuations are treated as zero (as there is no obligation due from the bank counterparty for the scenarios where the derivative has a negative MTM to the corporate).
EPE profiles vary between derivatives products
Different derivative products can have significantly different exposure profiles. Some derivatives, such as Cross Currency Swaps where there is a large cashflow at maturity, have an EPE profile that grows over the life of the trade and peaks towards maturity, shown in Figure 1. Other products, such as pay fixed Interest Rate Swaps (IRS), have an EPE profile that rises and falls over the life of the trade (similar to the "pull-to-par" effect on holding fixed income securities), peaking during the life of the trade, shown in Figure 2.
Figure 1: The EPE profile of a GBP100 million 5 year float-float Cross Currency Swap (pay USD, receive GBP) [Source: Bloomberg SWPM]
Figure 2: The EPE profile of a GBP100 million 5 year pay fixed Interest Rate Swap [Source: Bloomberg SWPM]
Bringing all components together – calculating CVA
Combining the EPE of the derivative with the PD profile of the counterparty and the LGD allows the CVA of the trade to be calculated. An approach to calculating CVA is shown as
EPEt = Present Value of Expected Positive Exposure at time t
PDt = Marginal probability of default between time t-1 and time t
LGD = Loss Given Default
As can be seen from the formula, each of the components described above acts as a driver of CVA. As would be expected, a higher EPE increases CVA, particularly for trades with an EPE profile that remains high until trade maturity, similar to that of the cross currency swap in Figure 1. Intuitively, a higher LGD and a higher PD both increase CVA, and so higher CDS spreads (where a standardised LGD is assumed the same for each bank counterparty) also indicate higher CVA. Finally, in most cases increasing the trade tenor would lead to an increase in CVA.
Quantifying the impact: Interest Rate Swaps
In order to illustrate the impact on trade value of counterparty credit, we consider a GBP100 million 5 year, pay fixed Interest Rate Swap (IRS). The EPE of the trade is that shown in Figure 2. Using an assumed LGD of 60 per cent, the implied 5 year PD can be estimated as 2.18 per cent for a counterparty with a flat 25bp CDS spread1. This rises to a 5 year PD of 12.39 per cent for a counterparty with a flat CDS spread of 150bp1.
The CVA for the IRS is shown for several different CDS levels in Figure 3. For a hypothetical counterparty with a flat CDS spread of 25bp, the CVA was found to be 0.010 per cent of trade notional. However, for a counterparty with a CDS spread of 150bp, the CVA was found to be 0.058 per cent. The implication is that the same trade with the less creditworthy counterparty would be worth approximately 5bp less than that with the more creditworthy counterparty. Alternatively, it could be said that the less creditworthy counterparty would need to offer a price around 5bp lower than the more creditworthy counterparty to offer the same economic value.
For comparison, as of 1st March 2019, the 5y CDS of major bank counterparties on the Bloomberg BANK CDS page ranged from 30bp to 153bp.
Figure 3: CVA as a percentage of trade notional for a GBP 5 year, pay Fixed interest rate swap for a range of different counterparty CDS levels. [Source: Bloomberg SWPM 29 March 2019]
The example shows that the CVA impact for Interest Rate Swaps is significant enough to warrant further consideration for the corporate treasurer, in particular regarding the economics of counterparty selection in view of the "true" fair value of derivatives. In fact, for trades with a higher share of cash flows at maturity such as Cross Currency Swaps, the impact of CVA is even greater than the IRS shown here. This is due to the more punitive EPE profile typically produced by these products. In the next and final article in the series, we further examine the pricing impact on different product types and illustrate the impact of trade tenor across a range of counterparty creditworthiness. Finally, we also consider the consequences of the pricing impact of CVA from an accounting perspective, in particular focussing on the impact on the corporate balance sheet and income statement.
1: Source: Bloomberg
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