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Derivatives

Derivatives are traditionally valued by taking the expected future cash flows and then discounting them in accordance with interest rates to give today’s value (present value).

Implicit is the assumption that the derivative contract will run to its contractual date and all the cash flows will be paid and received. However, in the real world this may not occur. The counterparty may default.

This has always been known but until the crisis of 2007/8 there was an assumption that large counterparties were risk free because they were too big to fail. This turned out to be a false assumption.

BIS defines Credit Value Adjustment as “an adjustment to the fair value (or price) of derivative instruments to account for counterparty credit risk (CCR). Thus, CVA is commonly viewed as the price of CCR.”

An example helps.

If you expect to receive a cash flow of \$10,000,000 in 1 years’ time and the interest rate used to discount the cash flow is 5% the present value is:

\$10,000,000 x 1/1.05 = \$9,523,809.52

Now assume that the 5% is a risk neutral rate (in practice it will be derived from a zero-coupon rate incorporating cash, swap or futures prices).

Our counterparty credit risk in our simple example would be \$9,523,809.52

In the real world, the valuation of a swap being the net of all the pay and receive amounts and the counterparty credit risk being the net value of all the swaps with the counterparty. This figure being marked against the counterparty limit.

The flaw in the approach is that it fails to consider the counterparty credit risk. If it deteriorates and you are owed money, there is a greater chance of loss.

Earlier the risk neutral rate was 5% but the counterparty’s credit risk may mean that its debt trades at a higher rate. For example, 6%.

This implies that we need to adjust for the credit risk.

\$10,000,000 x 1/1.06 = \$9,433,962.26

A Credit Value Adjustment of \$9,523,809.52-\$9,433,962.26 = \$89,847.25

The original counterparty credit valuation comprises \$9,433,962.26 for the derivative and \$89,847.25 for the CVA.

If the risk neutral rate alters that is one risk (market risk) if the counterparty credit spread changes that is another (credit risk). We can therefore decompose cash flows into two separate components that can be separately managed and accounted for.

What you can also see is that if the counterparty’s credit risk deteriorates the CVA charge increases.

That’s the theory. In practice the situation is made complex:

• Swaps can go in and out of the money as market rates change;

• Some derivatives may not create counterparty credit risk (for example options sold);

• The bank’s own credit spread will affect the CVA calculation (the cash flows paid out are worth less if the banks own credit risk deteriorates);

• Use of CVA in hedge accounting (IFRS 9) means that the relationship between the hedged item and the derivative may become harder to establish (or create greater P&L impact) because the credit spreads between the two are independent;

• Many banks mitigate credit exposures using collateral.

How you derive a CVA depends on the resources available and the complexity of the bank. To produce a straight forward CVA figure it is possible to map derivative cash flows to different credit curves that reflect their credit risks and this may suffice.

In other words, your system will contain multiple credit curves that reflect the credit risk of the receivable cash flows and a single curve that reflects your own creditworthiness to be used to discount payable cash flows.

The building of multiple curves will inevitably be subjective but single name credit default swap prices may be used or alternatively, generic yield curves for different credit ratings may be applied. What you use depends on the granularity you require.

More sophisticated models involve modelling the derivative over its life, using market volatilities and simulation and then applying default probabilities and loss given default assumptions.

Irrespective of the approach taken the models used are only as good as the data and assumptions made.

For example, how robust is the data for default probability, volatility and credit spreads? How frequently is the data captured? Are you using historic data or market prices? Who does the modelling and testing? Is CVA used for accounting and capital purposes or is there active management of the resultant credit risk?

These are just a few questions that are pertinent to a complex problem. Suffice to say that whilst accounting bodies and regulators want to see CVAs there is no one method that can be applied, where you can put your hand on your heart and say “it’s right”.

Like all risk measures knowing the weaknesses of your model are more important than knowing its strengths.