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

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  • 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.

Suggested Citation

  • Francesca Biagini & Alessandro Gnoatto & Katharina Oberpriller, 2025. "When defaults cannot be hedged: an actuarial approach to xVA calculations via local risk-minimization," Papers 2502.12774, arXiv.org, revised Feb 2025.
    • Handle: RePEc:arx:papers:2502.12774
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    References listed on IDEAS

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    1. Damiano Brigo & Andrea Pallavicini & Vasileios Papatheodorou, 2011. "Arbitrage-Free Valuation Of Bilateral Counterparty Risk For Interest-Rate Products: Impact Of Volatilities And Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 773-802.
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