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

Paper: arXiv 2502.12774

Authors: Francesca Biagini, Alessandro Gnoatto, Katharina Oberpriller

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly rigorous theoretical framework for xVA using local risk-minimization and BSDEs under unhedgeable default risk. However, it is purely mathematical without empirical validation or numerical backtesting in the excerpt provided.

Research Flowchart

  flowchart TD
    A[Goal: Price & Hedge xVA with Unhedgeable Default Jumps] --> B[Inputs: Market Risk Assets & Default Intensities]
    B --> C[Methodology: Apply Local Risk-Minimization Framework]
    C --> D[Computation: Formulate & Solve Quadratic BSDE]
    D --> E[Outcome: Optimal Hedging Strategy & Risk-Adjusted xVA Pricing]