The financial crisis forced the industry to reassess how counterparty credit risk impacts the valuation of a deal. Prior to the crisis, the practice of consolidating positions with one or two large, too big-to-fail institutions was considered safe, but the bankruptcy of Lehman Brothers, and subsequent stress on other large institutions, made it clear that this approach is not prudent. We are now seeing a move towards diversification to several counterparties and an increasing focus on the ability to quantify credit risk.

In a recent survey,^{1} over 43% of companies indicated that they are now required to calculate the credit value adjustment (CVA) for their derivative valuations. In addition, 50% of auditors stated that they require their clients to include a credit adjustment on more of their derivative positions now than in the past.^{2} Regulations, such as IFRS 7 and Topic 820 (formerly FAS 157), are driving demand for transparency and are based on the premise that trades are reported at fair value. To arrive at the fair market or exit values, companies must include the credit risk in their valuations and specifically report the CVA.

Many finance professionals had been using simple approaches that did not calculate this risk correctly for most derivatives positions. This article reviews the shortcomings associated with the simpler approaches and introduces a more robust method for more accurate measurement of CVA.

#### Credit Value Adjustment

Counterparty credit risk is the risk that a counterparty will default prior to the expiration of the trade and will be unable to make all contractual payments. As discussed above, fair value regulations require the inclusion of credit risk in the valuation of derivatives. CVA is one such measure of credit risk.

CVA is defined as the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. In other words, CVA represents the monetised value of the counterparty credit risk.

The general approach to determine CVA is to calculate the expected exposure profile to the counterparty as a function of time. The exposure profile should be evaluated at a portfolio level, including those trades that are part of a netting agreement with the counterparty and taking into account any requirements to post collateral (eg, a credit support annex to an International Swaps and Derivatives Association (ISDA) contract). The calculation of the expected exposure is determined using Monte Carlo simulation, modelling the volatility and correlation of the underlying market references, as well as the correlation between them and the possible default of the counterparty. Finally, to calculate the CVA, multiply the expected exposure by the default probability, and sum over all possible default times. The default probabilities used in this calculation can be implied from credit default swap spreads.

For most institutions, the inclusion of credit risk and calculation of CVA is generally done in one of two ways:

- Shifting (bumping) curves by the spread of the counterparty (or yourself).
- Analytically calculating the CVA (multiple approaches exist).

#### Shift (Bump) Curves

Many financial professionals have chosen, or have been advised, to include credit risk by shifting or bumping the curves and then revaluing the position. This approach in accomplished by following these steps:

- Value the position using the original unadjusted curve.
- Value the position using the adjusted curve.
- Calculate the difference between the original and adjusted curves. The result is the risk of default, or CVA.

The steps above illustrate that this is a very simple approach. However, it is suitable only for special cases. This approach is appropriate if you are calculating the CVA for a single instrument in which all the future cash flows are positive (i.e. receivables). For example, a long position in simple instruments, such as a bond or note. This simple method works for these types of instruments because the expected exposure at any future date is simply equal to the future value of the remaining cash flows – or in other words, the future value of the instrument. The cost of protecting that exposure can be approximated as the difference between the present value of the instrument discounted at the risk-free rate and that discounted at the risk-free rate plus the credit spread. In the case of fixed-rate bonds, this ‘bumping’ can be achieved by discounting at a yield equal to the Treasury yield (with appropriate maturity) plus the credit spread; in the case of floating rate notes, callable bonds or structured notes, it can be achieved by adding a discount margin or option adjusted spread (OAS) to the risk-free discounting rates.

Shifting the curve does not work, however, when it is possible for future cash flows to be either positive or negative, such as for swaps or forwards. In these cases, the correct approach for calculating CVA should take the volatility of underlying market references into account; otherwise the CVA will be understated.

#### Calculating CVA Using More Robust Methods

There are intermediate approaches to calculating CVA that do not require Monte Carlo simulation. These methods are available for certain simpler trades and assume that the market references (e.g. LIBOR) are not correlated with counterparty default. As many financial professionals value only simpler instruments, such as swaps and foreign exchange (FX) forwards, these intermediate approaches are sufficient in the majority of cases. For example, the CVA for a single non-collateralised vanilla fixed for floating interest rate swap can be calculated as the value of a portfolio of swaptions.

When two counterparties enter into a swap, it is possible for either party to default. This means that the counterparty risk can be bilateral. In other words, when a financial professional enters into a swap, they are implicitly short an option to default to the counterparty on its current and future obligations. Similarly, they are also long an option to default on their own obligations to the counterparty. The CVA in these two cases is called the CVA Charge and CVA Benefit, which reflect the market’s assessment of the credit risk of the counterparty defaulting and one defaulting, respectively.

So the adjusted fair value of the swap from the counterparties’ (typically a bank) perspective is: adjusted fair value = risk-free fair value ? bilateral CVA, where the bilateral CVA is the net of CVA Charge and Benefit.

The CVA Charge is the reduction in value of your assets (or potential assets) due to the possibility of default by your counterparty, and results in a negative impact on the balance sheet. The CVA Benefit, or debt value adjustment (DVA), is the reduction in value of your liabilities (or potential liabilities) due to the possibility of your own default and results in a positive impact on the balance sheet.

A swap that is currently valued near par can have both a CVA Charge and a CVA Benefit because it can potentially become either an asset or a liability.

#### Conclusion

As usual, with the introduction of new regulations comes a period of uncertainty in determining what will be an appropriate level of detail to ensure compliance. This can be seen with the various fair value regulations and specifically the credit risk calculations that are required, as a standard methodology has not been adopted leading some to adopt a less-than-thorough approach. Although there may be a tendency to use the simpler method and calculate credit value adjustments by bumping curves, this approach does not incorporate the appropriate level of credit risk for the most popular trades that are used by corporate treasuries and regional banks. Even if this practice has been acceptable to your auditors in the past, the use of this simple method increases the likelihood of future restatements.

The crisis of 2008 and the introduction of FAS 157/IFRS 7 have highlighted the need for finance professionals to have a better understanding of the credit risk associated with the deals they enter into or risk future questioning by stakeholders, auditors and possible restatement. Calculating the instruments’ credit risk using a more robust method can be just as easy to apply and provides a more accurate assessment of the fair value.

^{1 }Fincad Annual Corporate Finance Survey, 2010.

^{2} Fincad Annual Auditors Survey, 2010.

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