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Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests

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  • Alfonsi, Aurélien
  • Cherchali, Adel
  • Infante Acevedo, Jose Arturo

Abstract

This paper studies the multilevel Monte-Carlo estimator for the expectation of a maximum of conditional expectations. This problem arises naturally when considering many stress tests and appears in the calculation of the interest rate module of the standard formula for the SCR. We obtain theoretical convergence results that complement the recent work of Giles and Goda (2019) and give some additional tractability through a parameter that somehow describes regularity properties around the maximum. We then apply the MLMC estimator to the calculation of the SCR at future dates with the standard formula for an ALM savings business on life insurance. We compare it with estimators obtained with Least Squares Monte-Carlo or Neural Networks. We find that the MLMC estimator is computationally more efficient and has the main advantage to avoid regression issues, which is particularly significant in the context of projection of a balance sheet by an insurer due to the path dependency. Last, we discuss the potential of this numerical method and analyse in particular the effect of the portfolio allocation on the SCR at future dates.

Suggested Citation

  • Alfonsi, Aurélien & Cherchali, Adel & Infante Acevedo, Jose Arturo, 2021. "Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress tests," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 234-260.
    • Handle: RePEc:eee:insuma:v:100:y:2021:i:c:p:234-260
    DOI: 10.1016/j.insmatheco.2021.05.005
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    Cited by:

    1. Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How Many Inner Simulations to Compute Conditional Expectations with Least-square Monte Carlo?," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.

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    More about this item

    Keywords

    SCR; Multilevel Monte-Carlo; Nested Monte-Carlo; Stress tests; Asset liabilities management;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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