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Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples

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  • Maxim Bichuch
  • Agostino Capponi
  • Stephan Sturm

Abstract

We develop a novel framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no-arbitrage arguments, we derive the nonlinear backward stochastic differential equations (BSDEs) associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA which in turn identify a no-arbitrage interval. When borrowing and lending rates coincide we provide a fully explicit expression for the uniquely determined price of XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. This extends the result of Piterbarg by incorporating the effect of premature contract termination due to default risk of the trader and of his counterparty.

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  • Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2015. "Arbitrage-Free Pricing of XVA -- Part I: Framework and Explicit Examples," Papers 1501.05893, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1501.05893
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    References listed on IDEAS

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    4. Damiano Brigo & Andrea Pallavicini, 2014. "Nonlinear consistent valuation of CCP cleared or CSA bilateral trades with initial margins under credit, funding and wrong-way risks," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-60.
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    7. Roberto Blanco & Simon Brennan & Ian W. Marsh, 2005. "An Empirical Analysis of the Dynamic Relation between Investment‐Grade Bonds and Credit Default Swaps," Journal of Finance, American Finance Association, vol. 60(5), pages 2255-2281, October.
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    Cited by:

    1. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2015. "Arbitrage-Free Pricing of XVA - Part II: PDE Representation and Numerical Analysis," Papers 1502.06106, arXiv.org, revised Aug 2016.
    2. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.

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