Beyond Value-at-Risk: Wrong-Way-Risk Add-ons and Reverse Stress Testing

Abstract

The industry is currently seeking to evolve collateral models based on Value-at-Risk to include Wrong-Way-Risk (WWR) add-ons. A parallel trend is to require risk managers to possess Reverse Stress Testing (RST) tools to identify extreme but plausible scenarios and hedge them pro-actively. Use cases span a number of businesses including clearing, securities financing and uncleared margin rules.

We discuss the interrelation between WWR collateral add-ons and RST analytics in a handful of full-scale examples of clearing portfolios with about half-million equity derivative trades. We implement a structural, ground-up analysis based on a simulation with ten million scenarios with binary defaults. We use Stochastic Local Volatility models with Jumps (SLVJ models) for both the underlying equity risk factors and the credit of clearing members. We also use a standard multi-factor correlation model for credit and equity factors. Our RST analysis leads to detailed P&L attribution statistics specific to each extreme but plausible stress scenario.

We discuss 12 different collateral margining rules to study the impact of WWR add-ons. By comparing two policies with nearly equal total amounts of collateral allocation, the policy with WWR add-ons has a far greater degree of risk resilience.

Keywords: value-at-risk, wrong-way-risk, reverse stress testing, collateral, initial margin

JEL Classification: G12, G13, G24