Quantitative Financial Risk Management. Galariotis Emilios
applies the portfolio effects of netting and collateral, and aggregates exposure results to compute the average exposure along a term structure.
While an EPE may be a good indicator of the cost to replace a contract should the counterparty default, EPE is not helpful in the trade inception approval process because of its volatility and the need for a high confidence interval. Therefore, many banks will also report a very high percentile (e.g., 97.7th or 97.5th) of the exposure distribution over a large number of paths.
Note that these peaks in exposure profiles are not simply added over different products for a given counterparty, as these peaks may happen at different points in time. Rather, the time profiles of exposures are summed over products traded with a single counterparty, and the peak of that time profile is the summary PE measure. This methodology is conservative, as PEs are simply added over counterparties, while the bank may enter trades that mitigate each other in terms of PE with different counterparties.
We can readily see that CCR measurement necessarily combines the tools of standard market risk measurement with the tools of standard credit risk determination, a unique challenge to both. This frequently requires calculating probability-of-default (PD), loss-given-default (LGD), exposure-at-default (EAD), and a credit rating of the counterparty.4
The credit valuation adjustment (CVA) is defined as the product of the EPE times the LGD times the cumulative mortality rate (CMR), where the CMR is simply a multi-period PD rate. This is structurally equivalent to pricing EPE as the contingent leg of a credit default swap (CDS) by applying the counterparty spread to it. Such a spread is either a market quote if the name has a bespoke traded CDS, or a pseudo-CDS spread computed along a grid arrayed by region, industry, rating, and tenor. In the worst case, bond or loan spreads are used, giving rise to basis risk. It can be recognized that it is this part of the process that joins the market and the credit risk aspects of the algorithm. Practices for measuring market risk are used in mapping derivatives exposures to a set of market risk factors (e.g., spreads, volatilities, or correlations), simulating those factors out to a forward-looking time horizon, and determining the distribution of the level of exposures over various realizations of these risk factors in the simulation. Separately, standard credit risk processes provide assessments of the credit quality of the counterparty, such as PD and LGD estimation.
Direct or originating businesses (i.e., trading desks) are viewed as credit portfolios: As their positions get in the money, this gives rise to CCR, since the counterparty may default while owing money to the bank. The CVA represents a daily MTM transfer price of default risk charged to the originating business for insuring default risk, which is the price of a pseudo-CDS hedge with the EPE as underlying notional. The group (e.g., the market risk management department) that sells insurance to the business at inception of the trade will cover any loss due to counterparty default. As the exposure rises, due to either an increase in the position or a decrease in the credit quality of the counterparty, the CVA increases as it is marked to market. On the other hand, a profit is reported if the CVA decreases, due either to the bank's position becoming less in the money, an improvement in the counterparty's credit rating, or just the passage of time without any credit event. However, no further credit-related charges or costs are incurred by the business. In the limit, the CVA disappears as the maturity of the derivative contract is reached, and payment – if any is due – is made to the bank.
Products that are new or too complex to be properly simulated within the main CCR engine are dealt with “offline.” This usually means assigning them “risk factors” or more generally “add-ons” that are conservative and do not allow for netting; for this reason, such offline trades may account for up to 50 percent of the total exposure, although only 5 to 10 percent of trades made. The problem is that the counterparty credit exposure (CCE) is not sensitive to actual risk any longer: The sum of these add-ons may lead to the same measure of CCE for a set of offsetting trades as it does for a set of trades that have no offsets. Hence, these add-ons are really suited only for CCE with counterparties having single trades. Moreover, the large exposures they generate are not taken seriously by management, and these products do not undergo the complementary/downstream risk management processes such as stress testing, which results in risk measures that do not provide a comprehensive view of the risks that banks face. Worse still, management may increase limits for these products, aware that their CCR is overstated, thus defeating the purpose of these add-ons.
A relatively new but expanding practice is to model debt valuation adjustment (DVA) in the CCR framework, reflecting an institution's own option to default. Counterparties implicitly charge for an option to default, as when an institution holding a derivative position that is out of the money is in effect borrowing from the counterparty and implicitly pays for its outstanding liability through its credit spread. One way for a bank to fund its CVA would be to generate income from the sale of credit default swaps on itself, which cannot be done, hence the remaining portion of credit risk as reflected by the CVA. However, note that such “gut ” appeal DVA stems from the realization that if a bank enters a par swap agreement with a counterparty that has the same credit spread, then theoretically, credit risk considerations should not enter the pricing decision (i.e., the CVA and DVA should cancel for both parties in the transaction).
Analogous to the CVA, scenarios for underlying market factors are generated and averaged over the resultant negative portfolio marked-to-market values (liabilities), taking into account legal netting and collateral agreements. The resulting expected negative exposure, floored at zero if a bank gets in the money in any given scenario, is what risk managers expect to owe its counterparties on its derivative portfolio at the time of its default. It is priced as the contingent leg of a credit default swap using the bank's bank spreads, assuming that all deals are netted where possible, reflecting the fact that within the bank's jurisdiction it is likely that its counterparties would legally seek to net all positions upon its default.
For collateral considerations, often two types of default are considered. First, consider the case in which a bank defaults idiosyncratically, and a “springing” unilateral collateral agreement is assumed. This reflects the likely behavior of counterparties, who upon a worsening of a bank's credit worthiness will either demand to enter into unilateral collateral agreements where there are none or renegotiate existing collateral agreements to terms favorable to them. Second, there is the case of a systemic default, where a bank's default is part of a broad economic downturn. In this case it is much less clear that counterparties will be able to impose or change collateral agreements in their favor, and thus springing collateral is not considered. The final expected negative exposure value is a weighted average of the two cases, such that the relative weight is the relative likelihood of an idiosyncratic as opposed to a systematic default. These weights could be determined by the relative intensities of default implied by a bank's par spread curve and its risk premium spread curve backed using a capital asset pricing model methodology.
Review of the Literature
Supervisory rules and guidance on CCR can be found in the Basel Committee on Banking Supervision (BCBS) frameworks of Basel I (BCBS, 1988); Basel II (BCBS, 2006); Basel III (BCBS, 2011); and BCSB (2012). The U.S. Office of the Comptroller of the Currency (OCC) and the Board of Governors of the Federal Reserve System (BOG-FRS) issued supervisory guidelines (OCC & BOG-FRS 2011). Kang and Kim (2005) provide simple closed-form pricing models for floating-rate notes and vulnerable options under the CCR framework, deriving closed-form pricing models for them and illustrating the impact of the counterparty default intensity on the prices of floating-rate notes and vulnerable options.
Brigo and Chourdakis (2009) consider CCR for credit default swaps when default of the counterparty is correlated with default of the CDS reference credit. They incorporate credit spread volatility, adopt stochastic intensity models for the default events, and connect defaults through a copula function. The authors find that both default correlation and credit spread volatility have a relevant impact on the positive CCR valuation adjustment to be subtracted from the counterparty risk-free price. Jorion and Zhang (2009) observe that standard credit risk models cannot explain the observed clustering of default, sometimes described as “credit contagion,” and provide the first empirical analysis of credit contagion via direct counterparty effects. They find that bankruptcy announcements
See Araten and Jacobs 2001; Araten, Jacobs, and Varshney 2004; Araten, Jacobs, Varshney, and Pellegrino 2004; Carey and Gordy 2004; Carey and Hrycay 2001; Frye and Jacobs 2012; Jacobs 2010a, b; Jacobs and Kiefer 2010; and Jacobs, Karagozoglu, and Layish 2012.