Nov 7, 2011

Modeling Wrong Way Risk in CVA for Traders and Risk Managers

With traders and risk managers still facing many challenges and unanswered questions when it comes to Basel III compliance and the effective implementation of Credit Value Adjustment (CVA) practices, it’s no wonder that improving the ability to manage CVA is still keeping many practitioners awake at night.

In Part II of the Numerix CVA-inspired webinar series held on November 1st, Dr. Alexander Sokol, a specialist in this area and close integration partner of Numerix from CompatibL, focused on modeling wrong-way risk in CVA, and on using the Exposure Sampling Method as a practical tool for CVA trading and risk management. Dr. Sokol also discussed CVA hedging, noting that it isn’t about the default, but about hedging the sensitivity to credit spread and other market factors. “Credit spreads go up and down every day, increasing P&L volatility and masking the true performance of a firm’s OTC trading business,” Dr. Sokol explained.

Why Is Wrong Way Risk So Important?

Wrong way risk is a critical component of CVA for two reasons: 1) The world in which the counterparty is about to default is not the same as the world in which it did not default – thereby affecting the exposures, and 2) The world in which the counterparty already defaulted is even more different. “For fully collateralized counterparties, wrong way risk may create exposure and CVA where there was none before,” explained Dr. Sokol.

Managing Wrong Way Risk in CVA

Trading and risk managing wrong way risk in CVA requires a model that is easy to understand, fast and has stable calibration to market observables. “The traditional wrong way risk model does not meet these criteria because it depends on correlation of credit ‘to everything,' ” Dr. Sokol added.

The Exposure Sampling (ES) Method:  A Practical Tool for CVA Trading and Risk Management

“Exposure sampling is a way to manage CVA by treating portfolio exposure as just another derivative underlying,” Dr. Sokol explained. “It’s just like derivatives pricing.”

Using a traditional Derivative Pricing Model, we would choose a model for Equity or FX; calibrate it; and use it for pricing the contingent claim (derivative). Similarly, with the Exposure Sampling Model, we would choose a model for exposure; calibrate it; and use it for pricing the contingent claim (CVA). We would also choose between precise fit of “smile” (Dupire-like) vs. global fit (Heston/SABR-like).

 

 

Monte Carlo simulation of exposures is the first step in Exposure Sampling, in which we would simulate market observables; compute exposure with netting (but not CSA); and treat exposure and market observables the same way. When it comes to calibrating the Exposure Sampling Model, we would compute exposures for each day of a historical time interval, using only the cashflows that did not yet occur ‘as of today’; calculate structural or reduced form default model factors for each day of the same interval; and compute the historical correlation.

Hedging and Stress Testing CVA with Exposure Sampling

“CVA hedging is not only about the default, but also about the sensitivity to credit spread and other market factors,” Dr. Sokol reiterated.  “The actual defaults happen rarely?and their impact would be quantified by PFE, not CVA.”

Hedging wrong way risk with Exposure Sampling involves hedging a number, not a matrix. “Hedging a matrix of any kind is not possible in practice due to liquidity and transaction costs, while hedging a number is often possible,” Dr. Sokol explained. However, when hedging is impossible or incomplete, stress testing is considered to be key; and, it is better to be stress testing a number, not a matrix.

Stay tuned for the upcoming CVA-inspired webinars in this series, focusing on the art and science of advanced modeling of CSA and margin period of calculations on December 1st and December 15th.

To learn more, 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

Blog Post - Feb 21, 2012

Numerix presents “Stress Testing and Hedging CVA” at PRMIA

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