Oct 20, 2011

Modeling Wrong Way Risk in CVA for Quantitative Analysts

As market participants continue to evolve their trading and risk management practices, improving the ability to manage Credit Value Adjustment (CVA) is on the forefront for many institutions. To address these needs, Numerix is hosting a webinar series on the challenges of measuring and trading CVA for Quantitative Analysts. In the first webinar of this series, held on October 18th, Dr. Alexander Sokol, a specialist in this area and close integration partner of Numerix from CompatibL, discussed the following key topics: modeling wrong way risk in CVA, wrong way risk model calibration and hedging wrong way risk.

Current Modeling Challenges

Dr. Sokol began by discussing the modeling of wrong way risk in CVA within the Basel III framework. He presented a basic definition of CVA as “the change in portfolio value due to the possibility of counterparty default (unilateral or bilateral).” Dr. Sokol added that CVA is computed from first principles calculation by simulating both market evolution and credit events. Credit events are normally handled via forward probability, as in the Basel III formula and CVA trading analytics. While these are fast and accurate, they are not as flexible as first principles calculation.

 Dr. Sokol noted that expected positive exposure (EPE) in the CVA formula is conditional on default, a critical distinction that sometimes escapes the attention of quants modeling CVA. “The fact that the formula is conditional on default is a key element that is often overlooked,” he said. “This is exactly where wrong way risk enters into the picture,” he added.  “And, while the CVA formula above uses EPE conditional on default, it does not tell us how to compute it.”

The objective of Dr. Sokol’s discussion focused on an extension of the numerical integration method, which permits comprehensive wrong way risk modeling without compromising performance. He added that wrong way risk is a critical component of CVA for two reasons:

  • The world in which the counterparty is about to default is not the same as the world in which it did not default – affecting the exposures
  • The world in which the counterparty already defaulted is even more different

For fully collateralized counterparties, the default event itself may create exposure and CVA where there was none before, with collateral becoming insufficient with market shifts. A comprehensive model must include sources of wrong way risk, which are at work before and after default. This is difficult to accomplish within a framework which exclusively relies on forward probability of rare events. If the model requires simulation of rare events, it must not make the calculation prohibitively slow. Also, there is the performance challenge of first principles simulation of rare credit to be considered.

The Benefit of the Exposure Sampling Method for Wrong Way Risk in CVA

According to Dr. Sokol, “Exposure sampling is an extension of the CVA formula which includes full simulation of credit events, without paying the performance penalty.”  It includes sources of wrong way risk at work before or after default. It is a fast method with full credit simulation, rigorous calibration to the historical data and offers a robust way to hedge and stress test wrong way risk without trying to “hedge a matrix.”

CVA, you can access a replay of the webinar here. Also register now for the upcoming webinar on Modeling Wrong Way Risk in CVA for Traders and Risk Managers on November 1, 2011.

To learn more about modeling wrong way risk in CVA for Quantitative Analysts, contact sales@numerix.com


Other References:

“Lessons from the Financial Crisis: Insights from the Defining Economic Event of our Lifetime,” edited by Arthur M. Berd. The chapter that Dr. Sokol contributed to the Risk Books 2010 volume, is entitled, 'A Practical Guide to Monte Carlo CVA'.  Learn more.

Exposure Sampling for CVA – the Path to Full Simulation, CreditFlux.com article (2011)

Fast Monte Carlo CVA Using Exposure Sampling, Geneva RiskMinds 2010 conference presentation 
Stress testing and Hedging CVA, Risk Australia 2011 conference presentation
Modeling and Hedging Wrong Way Risk in CVA with Exposure Sampling, Risk USA 2011 conference presentation

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