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Sub-sampling and other considerations for efficient risk estimation in large portfolios

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

Abstract

Computing risk measures of a financial portfolio comprising thousands of derivatives is a challenging problem because (a) it involves a nested expectation requiring multiple evaluations of the loss of the financial portfolio for different risk scenarios and (b) evaluating the loss of the portfolio is expensive and the cost increases with its size. In this work, we look at applying Multilevel Monte Carlo (MLMC) with adaptive inner sampling to this problem and discuss several practical considerations. In particular, we discuss a sub-sampling strategy whose computational complexity does not increase with the size of the portfolio. We also discuss several control variates that significantly improve the efficiency of MLMC in our setting.

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  • 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.
    • Handle: RePEc:arx:papers:1912.05484
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    References listed on IDEAS

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    1. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    2. 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.
    3. Michael B. Giles, 2008. "Multilevel Monte Carlo Path Simulation," Operations Research, INFORMS, vol. 56(3), pages 607-617, June.
    4. Michael B. Giles & Kristian Debrabant & Andreas Ro{ss}ler, 2013. "Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation," Papers 1302.4676, arXiv.org, revised Jun 2019.
    5. 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.
    6. 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.
    7. Michael B. Giles & Abdul-Lateef Haji-Ali, 2018. "Multilevel nested simulation for efficient risk estimation," Papers 1802.05016, arXiv.org, revised Feb 2019.
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    Cited by:

    1. Michael B. Giles & Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Efficient Risk Estimation for the Credit Valuation Adjustment," Papers 2301.05886, arXiv.org.
    2. Abdul-Lateef Haji-Ali & Jonathan Spence, 2023. "Nested Multilevel Monte Carlo with Biased and Antithetic Sampling," Papers 2308.07835, arXiv.org.

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