payment. So, for example, a twenty-year interest rate swap with a mandatory break clause after five years will terminate five years after the start of the transaction with the mark-to-market value of the remaining fifteen years of the transaction paid in cash on the appropriate settlement date immediately after the mandatory break date. Ignoring credit risk, funding costs and capital considerations, the value of the two trades with and without the break clause will be the same. However, the expected exposure of the trade with a mandatory break is terminated after five years and hence the credit risk and CVA are much lower. In practice, trades with mandatory break clauses reduce the initial cost of the derivative for the counterparty and the trades are often restructured just prior to the break date. Figure 2.4 illustrates a swap with a break clause half way through the underlying term.
Figure 2.4 A swap with and without a break clause and the associated expected positive exposure profile. For the swap with the break clause, the CVA is lower.
Optional break clauses give the option to one or both counterparties to terminate the derivative on one or more dates prior to the natural maturity of the trade. Settlement then proceeds in the same way as a mandatory break clause, with a cash settlement of the mark-to-market of the remaining trade. In practice, optional break clauses have been rarely, if ever, exercised irrespective of any considerations of optimal exercise. The argument has been that exercising the break clause would ruin the relationship with the client. Internally within banks the right to exercise the credit break has often sat with client relationship management who have had few incentives to use the breaks.20 However, many derivative dealers are now arguing that optional break clauses should now be exercised and actively used as a credit mitigant (Cameron, 2012).
2.4.6 Buying Protection
The idea of buying “insurance” or “protection” against counterparty default is quite an old one. Bond insurance or financial guaranty insurance was introduced by American Municipal Bond Assurance Corp or AMBAC in 1971 (Milwaukee Sentinal, 1971). Municipal bond insurance is a type of insurance in which the bond insurer guarantees the interest and principal payments on a municipal bond. A number of bond insurance companies were created and they became known as monolines as they did not have other lines of insurance business. Bond insurance was a generally successful business but after the development of structured credit derivative products many bond insurers entered the credit derivatives market leading to significant losses. Ambac filed for protection from creditors under chapter 11 on 8 November 2010 (Ambac, 2010).
Credit default swaps offer the main means by which credit protection can be bought and sold, and as such are the primary mechanism for CVA trading desks to hedge out credit risks. Physically settled single name CDS contracts pay out the notional amount in exchange for a defaulted bond, although cash settled variants that pay
on default are also available. Hence, single name CDS provide a means of directly protecting a notional amount against the default of a specific counterparty. There are some complications in that the CDS is triggered by a number of specific default conditions and that some, like voluntary restructuring, are typically excluded. This means that the CDS does not always pay out when losses are taken. The Greek sovereign restructuring provides an example of this where the initial voluntary debt exchange did not trigger the sovereign CDS, only the later use of a ‘collective action clause’ triggered the CDS as it involved an element of coercion (Oakley, 2012).
CDS trade only a limited number of reference names and so in many cases buying single name CDS to hedge CVA is not possible. CDS indices such as the iTraxx and CDSIndex Company series can provide an alternative. These are liquidly traded indices which include a basket of underlying CDS contracts. They respond to changes in underlying perceptions of creditworthiness in the underlying basket of names and hence can be used to hedge general sensitivity to CDS spreads. Usually the members of a CDS index are also traded through the single name CDS market. CDS and CDS indices are discussed in Chapter 4 and active management of CVA in Chapter 22.
CHAPTER 3
CVA and DVA: Credit and Debit Valuation Adjustment Models
The only certainty is that nothing is certain.
3.1 Introduction
Recall the definition of CVA, given in equation (2.6). Re-arranging this formula gives
(3.2)
where in the second line I have introduced the notation,
This formula highlights that CVA is the adjustment to the underlying price of the derivative. In reality the full value of the derivative should include the impact of credit risk but CVA is treated separately for a number of reasons:
• CVA is normally calculated at a counterparty level and not at trade level. This follows from the existence of netting rules which mean that the value of a portfolio is typically netted together when calculating its value in the event of a default. If each individual trade were treated on an individual basis and the netting rules ignored then the CVA would be overestimated if a unilateral model is used (it could be over or underestimated in the case of a bilateral model but it will certainly be incorrect). Trade level CVA is possible but this requires a special technique and this is discussed in section 3.6.
• CVA is usually managed separately from the underlying derivative. CVA trade management is a very different activity from risk management of the underlying derivatives and requires different skills and experience. In addition derivative trading activities are normally aligned by asset class whereas CVA is counterparty aligned and crosses all asset classes.
• CVA is often accounted for separately in published accounts. This leads to a separation of internal financial reporting activity as well as book management.
As noted earlier, there are essentially two types of models for CVA: unilateral models that only consider the credit risk of the counterparty and bilateral models that consider the credit risk of both counterparty and self. Equation (3.1) is the definition of CVA in both cases. Funding costs add further complexity but these will be introduced later in Chapter 9. In the case of bilateral models it is useful to write
(3.3)
where CVA is a cost and DVA is a benefit. Bilateral CVA models naturally provide two terms, a term that reduces accounting value due to counterparty risk and a term that increases accounting value due to risk of own default, with the first term an integral over the expected positive exposure and the second an integral over the expected negative exposure, weighted by default probabilities. These two terms are frequently called CVA and DVA respectively, which can lead to confusion over the definition of CVA. Furthermore in certain institutions DVA is seen as the difference between a unilateral CVA model and a bilateral one, that is as the benefit from own credit risk. As we have already noted DVA is also used to refer to the accounting benefit from using the fair value accounting option on own issued debt. To avoid confusion
