When defaults cannot be hedged: an actuarial approach to xVA calculations via local risk-minimization

TL;DR

This paper addresses the challenge of pricing and hedging counterparty credit risk and funding in scenarios where default cannot be hedged, proposing an actuarial approach using local risk-minimization and BSDEs.

Contribution

It introduces a novel actuarial framework for xVA calculations that handles unhedgeable default risk using local risk-minimization and backward stochastic differential equations.

Findings

Provides a method to compute optimal hedging strategies without default hedging instruments.

Demonstrates the application of BSDEs in the context of unhedgeable default risk.

Offers insights into practical xVA valuation under realistic market constraints.

Abstract

We consider the pricing and hedging of counterparty credit risk and funding when there is no possibility to hedge the jump to default of either the bank or the counterparty. This represents the situation which is most often encountered in practice, due to the absence of quoted corporate bonds or CDS contracts written on the counterparty and the difficulty for the bank to buy/sell protection on her own default. We apply local risk-minimization to find the optimal strategy and compute it via a BSDE.