expected negative exposure enters the calculation of debit and funding valuation adjustments (DVA and FVA). The expected positive and negative exposure profiles for a five-year receivers interest rate swap are illustrated in Figure 2.1.
Figure 2.1 The expected positive and expected negative exposure profiles for a five-year interest rate swap with a notional of £100m at trade inception.
Given the exposure at the time default occurs, the amount recovered is usually expressed as a percentage, R, the recovery rate.14 Hence the recovered amount is given by
(2.4)
The recovery rate is commonly used in the credit derivatives market. The loss-given-default or LGD is often used in traditional credit risk and is simply one minus the recovery rate,
(2.5)
2.1.1 Wrong-way and Right-way Risk
Wrong-way risk is an important element of understanding credit exposure, although it is defined in a number of different ways. One traditional definition originating in credit risk modelling defines wrong-way risk as the risk that the exposure at default is larger than the exposure immediately prior to default. ISDA15 defines wrong-way risk in a much broader sense as occurring whenever the exposure to a counterparty is adversely correlated to the risk of the default of that counterparty (D’Hulster, 2001). This definition is the one most commonly applied in CVA modelling circles and is the one I use here. ISDA goes on to define specific wrong-way risk as associated with a particular transaction that has been poorly structured such as a repo agreement collateralised with the borrower's own bonds, and general or conjectural wrong-way risk as when credit quality and counterparty exposure are adversely linked through macro-economic factors. A simple example of this latter condition can be seen in the interest rate swaps market. A typical lending arrangement between a bank and a corporate counterparty involves a floating rate loan coupled with an interest rate swap in which the corporate pays fixed and receives a floating rate. The effective structure is then a fixed rate loan. In an economic recession interest rates typically fall at the same time that corporates experience a deterioration in their credit quality. The interest rate swap must be marked-to-market by the bank and as interest rates fall the value of the receiver swap increases, increasing the derivative exposure to the corporate. Hence this is an example of general wrong-way risk.
Right-way risk is the inverse of wrong-way risk and occurs whenever exposure and credit quality are favourably correlated. A classic example of this is a trade with a gold producer in which the exposure is linked to the gold price. As the gold price increases the exposure increases; however, the value of gold reserves also increases and hence the credit worthiness of the gold miner also increases. A deeper investigation of the gold miner case study is revealing. If the gold miner has sold forward all the remaining reserves at a low price, the increasing gold price would have no impact on the credit worthiness of the gold miner. The transactions may be off balance sheet and not readily visible to external analysis. In practice assessing wrong-way and right-way risk is a complex process and the co-dependence between counterparty and macro-economic factors difficult to estimate.
2.2 CVA and DVA: Credit Valuation Adjustment and Debit Valuation Adjustment Defined
Credit Valuation Adjustment or CVA is the market price of credit risk on a financial instrument that is marked-to-market, typically an OTC derivative contract. Hence CVA is defined as the difference between the price of the instrument including credit risk and price where both counterparties to the transaction are considered free of credit risk,
Note that as defined in equation (2.6) CVA will always be positive if we consider only the credit risk of the counterparty. This sign convention is the one often used by CVA management functions; however, note that the accounting impact of the same number is negative as in this case the credit risk reduces the value of the derivative so that
There are a variety of different models for CVA and the market uses models in which only the credit riskiness of the counterparty is considered (unilateral), and models in which the credit worthiness of both counterparties is considered (bilateral).
Bilateral CVA models add an additional term, Debit Valuation Adjustment or DVA that arises from the credit risk of the reporting institution. As the credit worthiness of the institution declines, usually marked through widening CDS spreads, the institution books an accounting gain on its derivative portfolio, with the gain reflecting the fact that should the reporting institution default it will not fully repay all its obligations. DVA is a very controversial topic as it acts to increase the accounting value of a portfolio of derivatives at the same time that the credit worthiness of the institution is declining. There is also considerable debate around whether DVA can be effectively hedged or monetised.
There are in fact two types of DVA appearing in accounts, derivative DVA, as described above and debt DVA that arises when an institution opts to fair value its own issued debt. In this case the institution books an accounting gain when their debt declines in value. In theory the institution could buy back the debt thus crystallising the gain, although in practice this does not often happen. The institution is unlikely to have funds available to buy back debt in such a scenario.
CVA was introduced as a financial reporting requirement under FAS 157 issued in September 2006 by the Financial Accounting Standards Board (FASB) and coming into force for all entities with fiscal years beginning after 15 November 2007. The requirement to consider credit risk was also introduced by the International Accounting Standards Board through IFRS 39 (IASB, 2004) that was endorsed by the European Commission in 2005. IAS 39, unlike FAS 157, did not explicitly state that own credit risk should be taken into account (McCarroll and Khatri, 2011). This was subsequently changed in IFRS 13 (IASB, 2012) and IFRS 9 (IASB, 2014).
2.3 The Default Process
While in simple terms default occurs when the counterparty fails to make a payment, in reality the process is a complex legal one that varies between legal jurisdictions. The case of the default of sovereigns and supranational entities is more complex still as it enters the domain of international law. The legal process can be a long one, lasting many years, particularly in the case of large multinational entities; Enron filed for bankruptcy protection on 2 December 2001 (BBC, 2002), however, the company did not emerge from bankruptcy until 14 July 2004 (Hays, 2004). This then poses two important questions; what types of default are there and when do we consider default to have occurred?
The Credit default swaps market has defined a number of different Credit Events that trigger the payout on CDS contracts on the defaulted entity. The 2003 ISDA Credit Derivatives Definitions (ISDA, 2003; Parker and Brown, 2003) sets out six different credit events:
• Bankruptcy
• Failure to pay
• Obligation acceleration
•
International Swaps and Derivatives Association.
