Recent events, including the default of Argentina, have emphasized the fundamental importance of incorporating the relatedness between the credit quality of a counterparty and the underlying market dependencies of a derivative transaction's mark-to-market value in calculations of credit exposure. More and more we view relatedness as a pervasive aspect of counterparty exposure in the credit and equity derivative markets, not only for foreign exchange derivatives. Though we acknowledge the view of David Rowe, group executive and v.p. for risk management at SunGard Trading and Risk Systems (DW, 4/14)) that a qualitative understanding of wrong-way risks in a portfolio can be achieved via a stress analysis, it is much more challenging to coherently integrate results generated in this fashion with a mark-to-market based hedging strategy.
The approach applied at JPMorganChase for computing fx wrong way exposure has previously been outlined in a Risk article in July 1999. Here we would like to emphasize more recent thinking and developments pertaining to the practical application of these ideas, concentrating on the following themes:
* the need for a consistent framework for relatedness
modeling across asset classes
* the advantages of a robust calculation approach that is
compatible with active risk management practices, passive
control-based risk mitigation strategies, and economic
capital measurement and allocation
* the desirability of a flexible model that can encompass both
historical and risk-neutral expectations about market behavior
* the importance of standardization of language about
counterparty credit risks in particular the notion of treating
exposure as a conditional on default quantity
First we will review the definitions and calculation philosophy that we view as fundamental to the treatment of counterparty credit risk. In order to admit a unified view of relatedness risk with other counterparty exposure, we have implemented a simulation approach. Complete market environments are generated by standard processes (used in derivative pricing applications) and enhanced Monte Carlo methods used to evaluate the high-dimensional integrals. The portfolio is revalued along the simulation paths allowing a direct determination of exposure if a counterparty defaults at a particular date along a particular future history of the world. Thus, correlation of market variables is treated directly, netting--where legally applicable--can be applied across products and different underlying market variables, path dependent products and physically settled options are naturally incorporated and complicated collateral agreements can be explicitly modeled.
Although computationally intensive, simulation facilitates a mathematically and conceptually consistent treatment of credit exposure across different types of products avoiding uncontrolled approximations. The basic risk measures computed include a time profile of expected exposures, exposure standard deviation and peak exposure (exposure at a particular confidence interval). Relatedness where appropriate is also factored into these calculations; all the exposure quantities are defined as conditional on default of a particular counterparty at a particular time which means, in principle, all market variables are conditioned on default before valuation of the trades with that counterparty.
The most significant advantage to simulation comes in the consistency it provides across the different risk management, control and decision processes. Expected exposure profiles and their credit spread implied price (along with sensitivities of these to market inputs) become the basis for hedging credit risk, marking the credit risk to market and associated profit and loss computations and for computing economic capital (with adjustments for exposure variability). Of course, the assignment of exposure to particular counterparties can be problematic when dealing with systematic risks; we would like to move toward a flexible view where exposure can be viewed jointly by name and by scenario.
In practical application of this methodology to the fx-relatedness, it became desirable to refine our basic approach. In a typical wrong-way fx transaction, a U.S. bank swaps country X currency for dollars with a major foreign bank in country X. When we consider the U.S. bank's exposure to the foreign bank we need to ask the question: what information does the fact that the foreign bank has defaulted give us about the dollar/currency X exchange rate?
This conditioning upon counterparty default involves separate consideration of scenarios in which the counterparty defaults for idiosyncratic reasons and defaults associated with a sovereign event. The essential input to this is a view on the distribution of fx rates for affected currencies when the sovereign defaults. This is used to adjust the simulated fx environment in the simulation model. At present, we represent the devaluation expectation by an expected stress amount (devaluation) and a time horizon over which the final currency slide occurs. Although the potential exists to imply these parameters from out-of-the-money fx option prices and estimates of default probabilities, there is insufficient liquidity in these options to make this a dependable approach across the variety of markets we need to address. For this reason, we are moving toward a blend of historical experience, and market insight about the currency regime to set the devaluation expectations.
Term Structure Devaluation
The most significant improvement we are making is to consider a term structure of devaluation. In our new treatment, the amount of assumed devaluation on sovereign default is phased in over a time horizon that is dependent on the likelihood of this event. By doing this we are focusing our risk-reward decisions on the most plausible paths to default even though the market may attribute finite probability to near instantaneous default from higher ratings. This has several advantages: 1) it recognizes the ability to hedge exposure and to terminate trading activity as the country gets downgraded, 2) it allows a smooth application of the fx-relatedness concept across the spectrum of country credit quality, rather than imposing an arbitrary quality threshold for the concept to be relevant, 3) it acknowledges the fact that by using market implied forward and volatility data our simulation methodology naturally captures short-term risk fairly efficiently.
Finally, we would like to mention efforts to apply a consistent relatedness framework across different asset classes. It is possible to identify several not entirely disjointed classes of relatedness that are all amenable to the same general scheme: 1) systematic events, e.g. country risk or industry downturns, that lead to large numbers of correlated defaults over a short time horizon and potentially large moves in market rates, 2) a counterparty with credit quality directly tied to a particular market rate, 3) pair-wise relatedness where the assets of a counterparty and a reference entity are correlated. Typical transactions fitting into this categorization might be for 1: portfolio credit derivatives or, as mentioned above, related fx trades, 2: commodity derivatives trades with a non-diversified producer of the same commodity, 3: equity or credit derivatives where the reference entity and counterparty are closely related.
Within the simulation methodology, these different flavors of relatedness can be encompassed in a reasonably comprehensive and efficient fashion. Credit spreads for the counterparties are co-diffused with the other market variables. This enables subtler forms of relatedness such as interest rate correlation with credit spreads to be automatically captured. In order to handle default conditional jumps we decompose counterparty spreads into components that are associated with systematic events or are shared with particular reference entities. These spread components allow us to assign probability weightings to different modes of default for the counterparty. Each default mode is associated with a move in relevant market rates or potentially in the near-simultaneous default of related credits.
A natural criticism of the approach sketched here is that it is overly elaborate and that it requires assignment of a large number of unobservable or difficult to estimate parameters. In fact, we view it as the simplest framework that is compatible with active management strategies and that gives a clear view to decision makers about the impact of increasingly complex risk mitigation features built into contracts.
Over time, the markets necessary for implying the input parameters will develop and a completely risk neutral pricing of these effects will become feasible. In the meantime, the model and its inputs provide a critical common communication language for those taking, evaluating, and hedging counterparty risk.
This week's Learning Curve was written by Andrew Abrahams, v.p. and head of derivatives research atJPMorgan in New York.
