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

Aurélien Alfonsi, Adel Cherchali and Jose Arturo Infante Acevedo

Insurance: Mathematics and Economics, 2021, vol. 100, issue C, 234-260

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.

Keywords: SCR; Multilevel Monte-Carlo; Nested Monte-Carlo; Stress tests; Asset liabilities management (search for similar items in EconPapers)
JEL-codes: C15 C63 G22 G32 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:100:y:2021:i:c:p:234-260

DOI: 10.1016/j.insmatheco.2021.05.005

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