Credit Valuation Adjustment: Opportunity to Enhance Credit Risk Management and Pricing

Imagine you’re a bank that has been active in the over-the-counter (OTC) derivatives market for the past decade. Although your exposure to counterparty credit risk is real, the management of exposure has been a secondary consideration to revenue growth. The International Swaps and Derivative Association (ISDA) observed that the notional amount outstanding in the OTC derivatives market grew seven-fold between 2000 and the end of June 2008, when the total amount reached US$637.7 trillion. At the time, this figure may have seemed like just another milestone on a chart moving endlessly upwards.

Yet by the end of December 2008, the total notional amount of OTC derivatives contracts outstanding was US$592 trillion. This was the first decline since the collection of data began in 1998. This transition from expansion to contraction, along with the uncertainty in global markets, would have likely led you to re-examine how you price credit risk in order to make better use of available capital.

Credit valuation adjustment (CVA) provides just such an opportunity. While the traditional means for banks to control credit risk has been setting limits on credit exposure and then checking that potential trades do not exceed set limits, CVA enables banks to price counterparty credit risk directly into trades, fully accounting for the cost of carrying or hedging the risk. Institutions wishing to implement CVA might naturally seek to incorporate it into their existing systems. However, many current trading systems cannot be easily extended for CVA. It therefore becomes important to understand how CVA fits into the bank’s methodology and to ensure it is being calculated by an appropriate system. When these two conditions are met, CVA will allow banks to free up capital, enable hedging strategies and minimise the volatility of earnings, thus facilitating future growth.

What is a CVA?

For years, standard industry practice was to mark derivative portfolios to market without taking the counterparty credit into account. All cash flows were discounted by the LIBOR curve, regardless of whether the trading counterparty was AA or BB. However, the true portfolio value must incorporate the possibility of losses due to counterparty default. In the case of a corporate bond, this is captured by discounting the cash flows on a spread above the risk-free rate, where the spread is a function of the creditworthiness of the issuer. CVA is, by definition, the difference between the risk-free derivative portfolio value and the true portfolio that takes into account the possibility of counterparty default. This adjustment can be positive or negative depending on which of the two counterparties (your own bank or the counterparty) is most likely to default and the in-the-moneyness of the portfolio.

The international accounting standard SFAS 157 requires banks to report the value of their derivative portfolio net of the credit valuation adjustment. In spite of credit mitigants in the form of netting and collateral, the CVA adjustments can be extremely large and changes in CVA from one reporting period to the next can have a material impact on overall profit and loss. For example:

Citigroup, Q1 2009 – A net income of US$1.6bn was recorded. This net income included a US$2.7bn credit valuation adjustment gain resulting primarily from the widening of Citigroup’s credit default swap spreads relative to counterparties.

AIG, Q4 2008 – As AIG received bailout funds from the Federal Reserve, credit spreads on the corporation narrowed, causing additional huge losses. AIG reported a US$6.7bn pre-tax (US$4.4bn after-tax) charge related to AIGFP’s credit valuation adjustment for mark-to-market (MtM) adjustments. This charge was a result of an increase in counterparty spreads and a decrease in AIG’s own credit spread, causing fair value losses on both AIGFP’s assets and liabilities.

Uses of CVA

The consistent and systematic application of counterparty-level CVA allows financial institutions to incorporate the pricing of credit risk into the pricing of derivative transactions, thereby leading to a more comprehensive pricing and capital management approach.

Such CVA adjustments will allow financial institutions to:

• Comply with international accounting regulations – International accounting regulations require financial institutions to report the MtM value of their trading book net of the CVA. By using a Monte Carlo simulation approach to measuring CVA that models portfolio diversification within and across asset classes, netting and collateral, financial institutions can report an accurate adjustment that can potentially be orders of magnitude less than an adjustment calculated as the simple sum of trade level CVAs.
• Manage market risk of CVA and reduce P/L volatility – Because CVA is an adjustment to the MtM value of the portfolio, volatility in CVA translates directly into P/L volatility. Consider the following example. A bank pays a fixed rate to its corporate clients and lays off this exposure by receiving fixed and paying floating to its inter-bank counterparties. In so doing its market risk is hedged. However, as corporate counterparties are generally less creditworthy than interbank counterparties, any rise in interest rates that increases the credit exposure to the corporate counterparties will increase the net CVA. These CVA swings due to changes in interest rates, foreign exchange rates and all other market risk factors can have a material impact on overall profit and loss. The systematic application of CVA at the counterparty level allows banks to hedge the market risk of CVA and reduce P/L volatility.
• Improve the pricing, hedging and transfer pricing of counterparty credit risk – Efficiently pricing counterparty credit risk helps ensure that profitable deals are taken on, risky deals are hedged effectively and traders are remunerated appropriately based on realistic transfer pricing. Calculation of CVA on a pre-deal basis can directly leverage any systems the bank might have to measure incremental credit exposure using simulation-based approaches.
• Evolve the bank’s risk culture – The use of CVA and CVA-adjusted VaR concepts will enable financial institutions to develop an integrated perspective of market and credit risk using consistent metrics. This will result in capital levels that properly account for the two risks in a consistent fashion. In addition, remuneration for front-office personnel will appropriately reflect the inherent credit-riskiness of the deals booked with various counterparts.
• Create more credit capacity and reduce capital consumption – Properly capturing the market price of credit risk allows financial institutions to expand the amount of business transacted with trading counterparties. Incorporating CVA concepts at the portfolio level can help to minimise the price charged for credit risk through the existence of market hedges in the portfolio, netting agreements and collateral agreements. The inclusion of CVA-related MtM effects in capital modeling has the potential to identify natural risk offsets, thereby reducing overall capital consumption.

Trade Level Versus Counterparty Level CVA

The credit exposure at the counterparty level is not the simple sum of trade level exposures due to portfolio diversification, netting and collateral agreements. In fact, it is generally much less than the simple sum. For this same reason, counterparty-level CVA, which must consider all the trades with a counterparty and uses risk-neutral scenarios for position valuation and pricing, can be very different from the sum of individual deal CVA and is generally considerably less than the sum of trade level CVAs. This comparison is illustrated in Figure 1 below.

Figure 1: Counterparty Level CVA

Figure 2: Sensitivity to IR Changes (Parallel Shift)

Figure 3: Impact on VaR

How is Counterparty-level CVA Calculated?

CVA can be calculated analytically for certain product types. In a unilateral case, the CVA adjustment is calculated assuming that the counterparty might default but that your own bank will never default. In the bilateral case, both counterparties might default. For the purposes of this overview, our examples will assume the unilateral case. For example, the CVA for a swap is closely related to the value of a swaption on the underlying exposure, which consequently increases the convexity of the interest rate exposure and impacts VaR (see Figures 2 and 3 above). But while CVA can be calculated analytically for certain product types, Monte Carlo simulation is the only practical alternative to measure counterparty-level CVA for real world multi-asset portfolios, as these simulations include netting and collateral agreements that span product and risk factor silos.

Conceptually, CVA modeling is a straightforward extension of the Monte Carlo-based simulation models used to estimate potential future exposure. This is illustrated in Figure 4 below. The valuation models used in step 2 and all the models used to incorporate the impact of netting and collateral in steps 3 to 6 are common. Exposure and CVA models also share common data inputs – market data, and terms and conditions for all trades and netting agreements, including credit support annex details, such as thresholds, call frequency and minimum transfer amounts.

Once the discounted exposure profile has been obtained, the calculation of CVA involves multiplying the discounted expected exposure in each time step by the risk-neutral probabilities of default and loss given default in that time step, and summing across all time steps over the life of the portfolio.

Figure 4: CVA Modelling

Systems Considerations

As financial institutions explore the feasibility of extending current simulation-based exposure models to calculate CVA, care must be taken to ensure that the straightforward conceptual extension is in fact a straightforward practical extension. These considerations help illustrate why many existing counterparty credit risk systems can’t be easily extended for CVA. Some of the more important factors include:

• Risk-neutral scenario generation – For the purposes of calculating CVA, risk-neutral scenarios are used rather than scenarios calibrated to historical data. The exposure model must be able to generate consistent risk-neutral scenarios across all asset types – interest rate, equity, foreign exchange (FX), credit and commodity. The inherent cross-asset nature of CVA modeling makes risk-neutral scenario generation considerably more challenging than in the single-asset class pricing context where well established risk-neutral pricing models are used.
• Exposure measures – In exposure models the primary output measures are typically 95% worst case exposure (netted and collateralised) that are then compared to limits for risk control and expected potential exposure (EPE) for economic capital. In CVA the primary output of the exposure model is a different measure – the discounted expected exposure. Simulation models that have been tuned to produce tail measures accurately do not necessarily produce accurate expectations without re-tuning.
• Accuracy – Many exposure models use crude pricing models and ignore essential elements of path dependency in the interest of bringing computational time within acceptable bounds. While these computational shortcuts may be acceptable for exposure modeling purposes, it is unlikely that they will be acceptable for CVA, which is primarily a pricing concept.
• Performance – The calculation of counterparty-level exposure requires revaluation of all derivative transactions across a few thousand Monte Carlo real world scenarios and a hundred or so time steps. The CVA calculation doubles this computational load, as the same set of trades needs to be revalued across a few thousand risk-neutral scenarios and a hundred or so time steps. To make matters worse, to hedge the P/L swings associated with CVA changes, the CVA desk needs to understand the sensitivity of CVA changes to all relevant market and credit risk factors. This can mean that the entire Monte Carlo simulation needs to run not just once or twice but rather hundreds of times per nightly batch run, in effect increasing the computational load by two orders of magnitude.
• Pre-deal capability – Many exposure models were fundamentally designed as batch systems without the capability to rapidly assess the incremental impact of a new what-if trade. In other words, they are fundamentally post-trade systems. On the other hand, CVA is fundamentally a pre- (and post-) trade concept, as CVA must be calculated pre-deal in order to factor it into the pricing of a trade and the selection of the counterparty.

Another potential starting point for CVA measurement is a front-office system. This is usually a non-starter, for many of the same reasons that they are not used for exposure simulation. Front-office systems are designed to value trades at the trade level. Therefore, any concept of producing counterparty-level exposures for real world portfolios where some positions net, some don’t, and some are subject to collateral agreements and others are not throws them off completely. And yet staying at the trade level is not an option to accurately manage CVA. In addition to the considerations outlined above, front-office systems present other barriers to CVA measurement, including an inability to simulate through time, performance limitations, and the fact any single trading system is not typically used for all the trades with a given counterparty.

Final Adjustments

While it may seem natural or even desirable to extend existing trading systems to calculate CVA, there are sufficient barriers in place that make this scenario unworkable. These systems do not have the ability to model netting and collateral agreements, generate the required risk-neutral scenarios across all risk factors, the performance levels required to complete CVA calculations and often process only a subset of all the trades with a counterparty. As a result, existing trading systems will most likely be a poor starting point to provide credible CVA measurement.

In fact, the requirements for CVA are better met by risk systems than their trading or front-office equivalents. A properly-engineered counterparty credit risk system that combines the pre-deal checks, precision and 24/7 operability of front-office systems with the performance and scenario-driven methodologies found in risk systems can be easily extended to CVA.

Banks should continue to investigate and implement approaches to enhance the pricing and measurement of credit risk. Through its ability to reduce P/L volatility, enable hedging strategies and create greater credit capacity, CVA, with the proper risk system in place to support it, provides just such an opportunity.