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Efficient Risk Estimation for the Credit Valuation Adjustment

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  • Michael B. Giles
  • Abdul-Lateef Haji-Ali
  • Jonathan Spence

Abstract

The valuation of over-the-counter derivatives is subject to a series of valuation adjustments known as xVA, which pose additional risks for financial institutions. Associated risk measures, such as the value-at-risk of an underlying valuation adjustment, play an important role in managing these risks. Monte Carlo methods are often regarded as inefficient for computing such measures. As an example, we consider the value-at-risk of the Credit Valuation Adjustment (CVA-VaR), which can be expressed using a triple nested expectation. Traditional Monte Carlo methods are often inefficient at handling several nested expectations. Utilising recent developments in multilevel nested simulation for probabilities, we construct a hierarchical estimator of the CVA-VaR which reduces the computational complexity by 3 orders of magnitude compared to standard Monte Carlo.

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  • Michael B. Giles & Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Efficient Risk Estimation for the Credit Valuation Adjustment," Papers 2301.05886, arXiv.org, revised May 2024.
    • Handle: RePEc:arx:papers:2301.05886
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    References listed on IDEAS

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    1. Michael B. Giles & Lukasz Szpruch, 2012. "Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without L\'{e}vy area simulation," Papers 1202.6283, arXiv.org, revised May 2014.
    2. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
    3. Michael Giles & Desmond Higham & Xuerong Mao, 2009. "Analysing multi-level Monte Carlo for options with non-globally Lipschitz payoff," Finance and Stochastics, Springer, vol. 13(3), pages 403-413, September.
    4. Michael B. Giles & Abdul-Lateef Haji-Ali, 2019. "Sub-sampling and other considerations for efficient risk estimation in large portfolios," Papers 1912.05484, arXiv.org, revised Apr 2022.
    5. Dereich, Steffen, 2021. "General multilevel adaptations for stochastic approximation algorithms II: CLTs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 226-260.
    6. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    7. K. Bujok & B. M. Hambly & C. Reisinger, 2015. "Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 579-604, September.
    8. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    9. Chang-Han Rhee & Peter W. Glynn, 2015. "Unbiased Estimation with Square Root Convergence for SDE Models," Operations Research, INFORMS, vol. 63(5), pages 1026-1043, October.
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    Cited by:

    1. Stéphane Crépey & Noufel Frikha & Azar Louzi & Jonathan Spence, 2024. "Adaptive Multilevel Stochastic Approximation of the Value-at-Risk [Approximation stochastique adaptative à plusieurs niveaux de la valeur à risque]," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04670735, HAL.
    2. Stéphane Crépey & Noufel Frikha & Azar Louzi & Gilles Pagès, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-04304985, HAL.
    3. Roberto Daluiso & Marco Pinciroli & Michele Trapletti & Edoardo Vittori, 2023. "CVA Hedging by Risk-Averse Stochastic-Horizon Reinforcement Learning," Papers 2312.14044, arXiv.org.
    4. St'ephane Cr'epey & Noufel Frikha & Azar Louzi & Gilles Pag`es, 2023. "Asymptotic Error Analysis of Multilevel Stochastic Approximations for the Value-at-Risk and Expected Shortfall," Papers 2311.15333, arXiv.org, revised Nov 2024.
    5. St'ephane Cr'epey & Noufel Frikha & Azar Louzi & Jonathan Spence, 2024. "Adaptive Multilevel Stochastic Approximation of the Value-at-Risk," Papers 2408.06531, arXiv.org.

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