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MVA: Initial Margin Valuation Adjustment by Replication and Regression

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  • Andrew Green
  • Chris Kenyon

Abstract

Initial margin requirements are becoming an increasingly common feature of derivative markets. However, while the valuation of derivatives under collateralisation (Piterbarg 2010, Piterbarg2012), under counterparty risk with unsecured funding costs (FVA) (Burgard2011, Burgard2011, Burgard2013) and in the presence of regulatory capital (KVA) (Green2014) are established through valuation adjustments, hitherto initial margin has not been considered. This paper further extends the semi-replication framework of (Burgard2013a), itself later extended by (Green2014), to cover the cost of initial margin, leading to Margin Valuation Adjustment (MVA). Initial margin requirements are typically generated through the use of VAR or CVAR models. Given the form of MVA as an integral over the expected initial margin profile this would lead to excessive computational costs if a brute force calculation were to be used. Hence we also propose a computationally efficient approach to the calculation of MVA through the use of regression techniques, Longstaff-Schwartz Augmented Compression (LSAC).

Suggested Citation

  • Andrew Green & Chris Kenyon, 2014. "MVA: Initial Margin Valuation Adjustment by Replication and Regression," Papers 1405.0508, arXiv.org, revised Jan 2015.
    • Handle: RePEc:arx:papers:1405.0508
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    References listed on IDEAS

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    1. 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.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    3. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    4. Daniel L. Thornton, 2009. "What the Libor-OIS spread says," Economic Synopses, Federal Reserve Bank of St. Louis.
    5. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.
    6. Chris Kenyon & Andrew Green, 2014. "VAR and ES/CVAR Dependence on data cleaning and Data Models: Analysis and Resolution," Papers 1405.7611, arXiv.org.
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    Citations

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    Cited by:

    1. 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.
    2. Tumasyan, Hovik, 2018. "A Second Look at Post Crisis Pricing of Derivatives - Part I: A Note on Money Accounts and Collateral," MPRA Paper 90806, University Library of Munich, Germany.
    3. Raymond Brummelhuis & Zhongmin Luo, 2018. "Arbitrage Opportunities in CDS Term Structure: Theory and Implications for OTC Derivatives," Papers 1811.08038, arXiv.org, revised Dec 2018.
    4. Chris Kenyon & Andrew Green, 2014. "Warehousing Credit (CVA) Risk, Capital (KVA) and Tax (TVA) Consequences," Papers 1407.3201, arXiv.org, revised Jan 2015.
    5. Simonella, Roberta & Vázquez, Carlos, 2023. "XVA in a multi-currency setting with stochastic foreign exchange rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 59-79.
    6. Lucia Cipolina Kun & Simone Caenazzo & Ksenia Ponomareva, 2020. "Mathematical Foundations of Regression Methods for the approximation of the Forward Initial Margin," Papers 2002.04563, arXiv.org, revised Sep 2022.
    7. Wujiang Lou, 2015. "MVA Transfer Pricing," Papers 1512.07337, arXiv.org, revised Jul 2016.
    8. Lixin Wu & Dawei Zhang, 2020. "xVA: DEFINITION, EVALUATION AND RISK MANAGEMENT," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-24, February.
    9. Andrew Green & Chris Kenyon, 2014. "KVA: Capital Valuation Adjustment," Papers 1405.0515, arXiv.org, revised Oct 2014.

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