At the end of May 2011, the International Swaps and Derivatives Association (ISDA) published new analysis of the over-the-counter (OTC) derivatives market. While the analysis showed a 12% decline in the notional outstanding, from $475 trillion in 2007 to $419 trillion in 2010, this decline does not necessarily indicate a change in new OTC derivatives market. Conrad Volstad, ISDA CEO, commented that portfolio compression had had a significant impact on outstanding volumes as market participants looked to reduce credit risk, adding that the industry’s collaborative work on documentation, netting and collateral was also having a ‘major impact’ in reducing risk in the markets.
The use of practices like portfolio aggregation, collateral and netting clearly demonstrates the ongoing importance to banks of accurate exposure measurement in calculating their counterparty credit risk.
For OTC derivatives, this quantification is also known as potential future exposure (PFE). PFE quantifies the counterparty risk/credit risk by evaluating trades already done against possible market prices in the future, over the lifetime of the transactions. Much has been written on the theory of PFE, but it is about much more than theory. Over the last decade, banks have made significant investments in hardware, software and operations, building ever-more sophisticated PFE measurement systems. Throwing increasing amounts of technology at this area, however, will not in itself provide the total solution.
The most sophisticated methodology currently available to estimate possible future outcomes and calculate PFE as a statistic is the full Monte Carlo simulation. It simulates the underlying market data over the life of the portfolio and price each contract at selected time steps as it matures. Since the evolution of future market data is not deterministic, Monte Carlo simulations are used to generate a large number of possible paths, and PFE is calculated as a statistic based on these outcomes.
The simulation method handles the full pricing of complex contracts and the correct modeling of path-dependent pay-offs when the contracts are aged over their life. Diversification and hedging effects within the netting set are fully simulated and the method allows for a good approximation of the effect of credit risk mitigation provided by collateral agreements. The main drawback is that the simulation method is both data and computationally intensive. In addition to investing in significant IT resources, the bank will also need to assign functional experts to maintain the parameterization of the engine and ensure that the results make sense.
Several precursors are required before any results can be obtained: To prepare for Monte Carlo simulation the bank needs to collect and clean a sufficiently long market data history. The data aging models that will be used to generate the range of possible future market data paths are calibrated on this history and correlation matrices need to be computed. Once the parameterization has been done and approved, the actual simulation can be run. The number of simulation steps is determined by reporting requirements; the number of paths depends on the convergence of the Monte Carlo algorithm. A clear challenge is that standard pricing libraries cannot be reused without modification. Whereas most standard pricing functions provide mark-to-market prices and sensitivities, pricing for PFE must handle aging through time and take into account the eventual path dependency. Moreover, the pricing models used in the front-office may be too slow for PFE simulation and have to be approximated. They may need to be simplified, ideally replacing numerical methods by closed form expressions. A separate pricing function library suitable for PFE simulation will therefore have to be maintained. This will add cost and delay the time to market for new products, especially if the latter are not standardized. This challenge is particularly difficult to overcome for structured and securitization products
The more traditional add-on method expresses the PFE as the sum of two terms: the ‘current value’ and the ‘add-on’, with the latter representing a possible future increase in the contract’s value over today’s value. In most frameworks the current value of the contract is defined as its mark-to-market value, but it could also be the book value, derived from the accounting systems. There are several ways of estimating the add-on. It is frequently calculated by multiplying the nominal amount of the contract with a risk weighting which is selected from a look-up table linked to some of the contract’s characteristics.
This approach has also some drawbacks: they do not adapt as quickly to changing market conditions; they are more approximate in modeling the impact of credit risk mitigation techniques; and they generally provide a higher exposure, and hence capital requirement, since they are set to be more conservative. For many types of exposure, however, these analytical methods are fast, sufficiently transparent and largely accurate enough. They provide a stable and reliable methodology.
But how do we have to choose the appropriate methodology and how do we have to put forward criteria which could be used in making this decision?
In short, the optimal solution for a bank needs to satisfy two questions:
• Can I justify the figures obtained?
• Are these figures sufficiently risk sensitive?
Exposure figures are used to monitor the bank’s operations and as a basis for decisions. The larger or more complex an exposure, the more important it is that the risk manager can justify the figure and explain how it was obtained. Similarly, the larger or more complex an exposure, the more important it is that the exposure measure adjusts through time and differentiates between specific instrument and counterparty criteria.
The following table lists some of the possible decision criteria that can be used by the bank to split the PFE calculations for off-balance sheet derivatives into smaller parts. The latter can then be combined to produce the overall exposure figure.
These criteria are not independent. For example, the deal may be based on a complex path dependent product, but in the overall context its exposure is insignificant compared with exposure to other counterparties. It might therefore be sufficient to estimate the PFE for this deal using a simple fixed add-on.
Some structured products present a particular challenge. State-of-the-art trading systems have flexible structuring tools embedded within them. The flexibility that is now available in the front-office is not, however, carried through to the PFE simulator. From a technical point of view it is rarely possible to plug these tools directly into a full, Monte Carlo-based portfolio simulation.
A further challenge in the case of structured products may be the computational time required; a simpler functional model may not be acceptable to simulate the exposure. This can be addressed by trying to tune the technical framework (for example via gridification, cache memory, or use of specialized hardware), but the hypothetical example shown below demonstrates that this will not always provide the answer:
Imagine that a single price takes one minute to compute; the simulation requires 5000 paths and 30 time steps; and the maximum time window available is four hours. Then (assuming linear scaling), only eight paths can be run per processor core. To provide the computing power for this single deal, 625 processors would be required. To handle 120 deals of this type, the bank would require 75 000 cores – a situation which is just not feasible in practice.
So, the bank needs to use a two step approach: first, apply an add-on method in order to approve the trade and include it in the daily process; then, when available, move to a more complex approach for monitoring it through its life cycle.
Use of the add-on approach brings its own questions, however. How do I set prudent but accurate add-ons? What level of ‘granularity’ should they have – in other words, do I define add-ons by type of instrument, by currency, by maturity and/or by other criteria? How often should these add-ons be reviewed?
A number of methods can be used to estimate the add-on for PFE, some more complex than others. Three methods, based on the Basel II approach to calculating the exposure at default (EAD) for OTC derivatives are a good starting point. Additionally, specific ‘shocks’ may be applied to the underlying market factors. These may be fully deterministic or may take scenarios from a historical period, possibly a historical period of significant stress like the add-on through stress testing and via historical simulation.
The optimal approach for banks calculating PFE for OTC derivatives is a combined approach, applying Monte Carlo simulations for the largest and most complex exposures where they bring real value, but using analytical methods for other exposures, and taking advantage where appropriate of a combination of add-on plus simulation methods, such as Basel II Internal Model Method (IMM). The IMM is the most sophisticated of the three Basel methods and assumes that the bank can run a full simulation of PFE for the transaction, or set of transactions.
Success depends ultimately on risk managers knowing their business and being able to ‘slice and dice’ when quantifying PFE to best reflect the different elements of the bank’s exposure.
Business Specialist Credit and Market Risk EMEA Region
Senior Functional Architect
 ISDA, OTC Derivatives Market Analysis Year-end 2010, May 2011.
 BIS, Basel II: International Convergence of Capital Measurement and Capital Standards:
A Revised Framework – Comprehensive Version, Annex 4, June 2006