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Everything You Always Wanted to Know About XVA Model Risk but Were Afraid to Ask

Author

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  • Lorenzo Silotto
  • Marco Scaringi
  • Marco Bianchetti

Abstract

Valuation adjustments, collectively named XVA, play an important role in modern derivatives pricing to take into account additional price components such as counterparty and funding risk premia. They are an exotic price component carrying a significant model risk and computational effort even for vanilla trades. We adopt an industry-standard realistic and complete XVA modelling framework, typically used by XVA trading desks, based on multi-curve time-dependent volatility G2++ stochastic dynamics calibrated on real market data, and a multi-step Monte Carlo simulation including both variation and initial margins. We apply this framework to the most common linear and non-linear interest rates derivatives, also comparing the MC results with XVA analytical formulas. Within this framework, we identify the most relevant model risk sources affecting the precision of XVA figures and we measure the corresponding computational effort. In particular, we show how to build a parsimonious and efficient MC time simulation grid able to capture the spikes arising in collateralized exposure during the margin period of risk. As a consequence, we also show how to tune accuracy vs performance, leading to sufficiently robust XVA figures in a reasonable time, a very important feature for practical applications. Furthermore, we provide a quantification of the XVA model risk stemming from the existence of a range of different parameterizations according to the EU prudent valuation regulation. Finally, this work also serves as an handbook containing step-by-step instructions for the implementation of a complete, realistic and robust modelling framework of collateralized exposure and XVA.

Suggested Citation

  • Lorenzo Silotto & Marco Scaringi & Marco Bianchetti, 2021. "Everything You Always Wanted to Know About XVA Model Risk but Were Afraid to Ask," Papers 2107.10377, arXiv.org, revised Mar 2025.
  • Handle: RePEc:arx:papers:2107.10377
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    File URL: http://arxiv.org/pdf/2107.10377
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    References listed on IDEAS

    as
    1. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    2. 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.
    3. Damiano Brigo & Agostino Capponi & Andrea Pallavicini, 2014. "Arbitrage-Free Bilateral Counterparty Risk Valuation Under Collateralization And Application To Credit Default Swaps," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 125-146, January.
    4. Andrea Pallavicini & Daniele Perini & Damiano Brigo, 2012. "Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments," Papers 1210.3811, arXiv.org, revised Dec 2012.
    5. Caspers, Peter & Giltinan, Paul & Lichters, Roland & Nowaczyk, Nikolai, 2017. "Forecasting initial margin requirements: A model evaluation," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 10(4), pages 365-394, October.
    6. Andrew Green & Chris Kenyon, 2014. "MVA: Initial Margin Valuation Adjustment by Replication and Regression," Papers 1405.0508, arXiv.org, revised Jan 2015.
    7. Henrard, Marc, 2007. "The irony in the derivatives discounting," MPRA Paper 3115, University Library of Munich, Germany.
    8. Andrea Maran & Andrea Pallavicini & Stefano Scoleri, 2021. "Chebyshev Greeks: Smoothing Gamma without Bias," Papers 2106.12431, arXiv.org.
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    Cited by:

    1. Cyril B'en'ezet & St'ephane Cr'epey, 2022. "Handling model risk with XVAs," Papers 2205.11834, arXiv.org, revised Aug 2024.

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