Option-Based Pricing of Wrong Way Risk for CVA

TL;DR

This paper introduces a practical, option-based worst-case approach for managing wrong way risk in CVA, addressing calibration and hedging challenges with a novel model and efficient optimization methods.

Contribution

It develops a finite-variance worst-case model for WW-CVA using static option hedging, improving realism and practical risk management.

Findings

Option-based hedging significantly reduces WW-CVA.

Theoretical WW-CVA is unbounded, but practical bounds are achievable.

Efficient methods for optimizing hedges are presented.

Abstract

The two main issues for managing wrong way risk (WWR) for the credit valuation adjustment (CVA, i.e. WW-CVA) are calibration and hedging. Hence we start from a novel model-free worst-case approach based on static hedging of counterparty exposure with liquid options. We say "start from" because we demonstrate that a naive worst-case approach contains hidden unrealistic assumptions on the variance of the hazard rate (i.e. that it is infinite). We correct this by making it an explicit (finite) parameter and present an efficient method for solving the parametrized model optimizing the hedges. We also prove that WW-CVA is theoretically, but not practically, unbounded. The option-based hedges serve to significantly reduce (typically halve) practical WW-CVA. Thus we propose a realistic and practical option-based worst case CVA.