Economic Scenario Generators: a risk management tool for insurance
MathematicS In Action, Volume 11 (2022) no. 1, pp. 43-60.

We present a risk management tool, named Economic Scenario Generator (ESG), used by insurance companies for simulating the global state of one or several economies described by key financial risk drivers. This tool is of particular use within the Solvency II framework, since insurance companies are required to value their balance-sheet from a market-consistent viewpoint. However, there is no observable price of insurance contracts hence the necessity of relying on ESGs to perform Monte Carlo simulations useful for valuation. As such, the calibration of Risk-Neutral models underlying this valuation is of particular interest as there is a strong requirement to match observable market prices. Furthermore, for a variety of applications, the insurance company has to value its balance-sheet over a set of different economic conditions, leading to the need of intensive re-calibrations of such models. In this paper, we first provide an overview of the key requirements from Solvency II and their practical implications for insurance valuation. We then describe the different use cases of ESGs. A particular attention is paid to Risk-Neutral interest rates models, specifically the Libor Market Model with a stochastic volatility. We discuss the complexity of its calibration and describe fast calibration methods based on approximations and expansions of the probability density function. Comparisons with more common method highlight the reduction in calibration time.

Published online:
DOI: 10.5802/msia.16
Classification: 91-10,  60G99
Keywords: Insurance, Solvability II, Risk management, Economic Scenarios Generators, LIBOR Market Model
Pierre-Edouard Arrouy 1; Alexandre Boumezoued 1; Bernard Lapeyre 2; Sophian Mehalla 1

1 Milliman, 14 Avenue de la Grande Armée, 75017, Paris, France
2 École des Ponts ParisTech, 6-8 avenue Blaise-Pascal 77455 Marne-la-Vallée, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Pierre-Edouard Arrouy and Alexandre Boumezoued and Bernard Lapeyre and Sophian Mehalla},
     title = {Economic {Scenario} {Generators:} a risk management tool for insurance},
     journal = {MathematicS In Action},
     pages = {43--60},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {11},
     number = {1},
     year = {2022},
     doi = {10.5802/msia.16},
     language = {en},
     url = {}
AU  - Pierre-Edouard Arrouy
AU  - Alexandre Boumezoued
AU  - Bernard Lapeyre
AU  - Sophian Mehalla
TI  - Economic Scenario Generators: a risk management tool for insurance
JO  - MathematicS In Action
PY  - 2022
DA  - 2022///
SP  - 43
EP  - 60
VL  - 11
IS  - 1
PB  - Société de Mathématiques Appliquées et Industrielles
UR  -
UR  -
DO  - 10.5802/msia.16
LA  - en
ID  - MSIA_2022__11_1_43_0
ER  - 
%0 Journal Article
%A Pierre-Edouard Arrouy
%A Alexandre Boumezoued
%A Bernard Lapeyre
%A Sophian Mehalla
%T Economic Scenario Generators: a risk management tool for insurance
%J MathematicS In Action
%D 2022
%P 43-60
%V 11
%N 1
%I Société de Mathématiques Appliquées et Industrielles
%R 10.5802/msia.16
%G en
%F MSIA_2022__11_1_43_0
Pierre-Edouard Arrouy; Alexandre Boumezoued; Bernard Lapeyre; Sophian Mehalla. Economic Scenario Generators: a risk management tool for insurance. MathematicS In Action, Volume 11 (2022) no. 1, pp. 43-60. doi : 10.5802/msia.16.

[1] Directive 2009/136/EC of the European parliament and of the council, Official Journal of the European Union, Volume 337 (2009), p. 11

[2] Directive 2009/138/EC of the European Parliament and the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II) (2009) (Technical report) | DOI

[3] EIOPA Insurance stress test 2014 (2014) (Technical report)

[4] Guidelines on the valuation of technical provisions (2015) (Technical report)

[5] Damien Ackerer; Damir Filipović; Sergio Pulido The Jacobi stochastic volatility model, Finance Stoch., Volume 22 (2018), pp. 667-700 | DOI | MR | Zbl

[6] Hansjörg Albrecher; Daniel Bauer; Paul Embrechts; Damir Filipović; Pablo Koch-Medina; Ralf Korn; Stéphane Loisel; Antoon Pelsser; Frank Schiller; Hato Schmeiser et al. Asset-liability management for long-term insurance business, Eur. Actuar. J., Volume 8 (2018) no. 1, pp. 9-25 | DOI | MR | Zbl

[7] Aurélien Alfonsi; Adel Cherchali; Jose Arturo Infante Acevedo A synthetic model for asset-liability management in life insurance, and analysis of the SCR with the standard formula, Eur. Actuar. J., Volume 10 (2020) no. 2, pp. 457-498 | DOI | MR | Zbl

[8] Pierre-Edouard Arrouy; Alexandre Boumezoued; Bernard Lapeyre; Sophian Mehalla Jacobi Stochastic Volatility factor for the Libor Market Model (2020) (

[9] Autorité de contrôle prudentiel et de résolution Générateurs de scénarios économiques : points d’attention et bonnes pratiques (2020) (

[10] Daniel Bauer; Andreas Reuss; Daniela Singer On the calculation of the Solvency Capital Requirement based on nested simulations, ASTIN Bull., Volume 42 (2012) no. 02, pp. 453-499 | MR | Zbl

[11] Elia Berdin; Helmut Gründl; Christian Kubitza Rising interest rates, lapse risk, and the stability of life insurers (2017) (Technical report)

[12] Paul Bonnefoy-Cudraz Implémentation et calibrage d’un Générateur de Scénarios Economiques: impact sur la volatilité du Solvency Capital Requirement (2016) (Mémoire, EURIA)

[13] Fabrice Borel-Mathurin; Julien Vedani Market-Consistent valuation: a step towards calculation stability (2019)

[14] Damiano Brigo; Fabio Mercurio Interest rate models-theory and practice: with smile, inflation and credit, Springer, 2007

[15] Marcus C Christiansen; Andreas Niemeyer et al. Fundamental definition of the solvency capital requirement in Solvency II, ASTIN Bull., Volume 44 (2014) no. 3, pp. 501-533 | DOI | MR | Zbl

[16] Harald Cramér Mathematical methods of statistics (PMS-9), 9, Princeton University Press, 1946 | DOI

[17] Christa Cuchiero; Martin Keller-Ressel; Josef Teichmann Polynomial processes and their applications to mathematical finance, Finance Stoch., Volume 16 (2012) no. 4, pp. 711-740 | DOI | MR | Zbl

[18] Yiran Cui; Sebastian del Baño Rollin; Guido Germano Full and fast calibration of the Heston stochastic volatility model, Eur. J. Oper. Res., Volume 263 (2017) no. 2, pp. 625-638 | MR | Zbl

[19] Laurent Devineau; Pierre-Edouard Arrouy; Paul Bonnefoy; Alexandre Boumezoued Fast calibration of the Libor Market Model with Stochastic Volatility and Displaced Diffusion, J. Ind. Manag. Optim., Volume 16 (2020) no. 4, pp. 1699-1729 | DOI | MR | Zbl

[20] European Parliament Delegated Acts, Official Journal of the European Union (2014)

[21] Anthony Floryszczak; Olivier Le Courtois; Mohamed Majri Inside the Solvency 2 black box: net asset values and solvency capital requirements with a least-squares Monte-Carlo approach, Insur. Math. Econ., Volume 71 (2016), pp. 15-26 | DOI | MR | Zbl

[22] Farshid Jamshidian LIBOR and swap market models and measures, Finance Stoch., Volume 1 (1997) no. 4, pp. 293-330 | DOI | Zbl

[23] Hal Pedersen; Mary Pat Campbell; Stephan L. Christiansen; Samuel H. Cox; Daniel Finn; Ken Griffin; Nigel Hooker; Matthew Lightwood; Stephen M. Sonlin; Chris Suchar Economic scenario generators: a practical guide (2016) (Technical report)

[24] Julien Vedani; Nicole El Karoui; Stéphane Loisel; Jean-Luc Prigent Market inconsistencies of Market-Consistent European life insurance economic valuations: pitfalls and practical solutions, Eur. Actuar. J., Volume 7 (2017) no. 1, pp. 1-28 | DOI | MR | Zbl

[25] Lixin Wu; Fan Zhang LIBOR Market Model with stochastic volatility, J. Ind. Manag. Optim., Volume 2 (2006) no. 2, pp. 199-227 | MR | Zbl

Cited by Sources: