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.
Mots clés : Insurance, Solvability II, Risk management, Economic Scenarios Generators, LIBOR Market Model
@article{MSIA_2022__11_1_43_0,
author = {Arrouy, Pierre-Edouard and Boumezoued, Alexandre and Lapeyre, Bernard and Mehalla, Sophian},
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 = {http://www.numdam.org/articles/10.5802/msia.16/}
}
TY - JOUR AU - Arrouy, Pierre-Edouard AU - Boumezoued, Alexandre AU - Lapeyre, Bernard AU - Mehalla, Sophian TI - Economic Scenario Generators: a risk management tool for insurance JO - MathematicS In Action PY - 2022 SP - 43 EP - 60 VL - 11 IS - 1 PB - Société de Mathématiques Appliquées et Industrielles UR - http://www.numdam.org/articles/10.5802/msia.16/ DO - 10.5802/msia.16 LA - en ID - MSIA_2022__11_1_43_0 ER -
%0 Journal Article %A Arrouy, Pierre-Edouard %A Boumezoued, Alexandre %A Lapeyre, Bernard %A Mehalla, Sophian %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 %U http://www.numdam.org/articles/10.5802/msia.16/ %R 10.5802/msia.16 %G en %F MSIA_2022__11_1_43_0
Arrouy, Pierre-Edouard; Boumezoued, Alexandre; Lapeyre, Bernard; Mehalla, Sophian. Economic Scenario Generators: a risk management tool for insurance. MathematicS In Action, Tome 11 (2022) no. 1, pp. 43-60. doi : 10.5802/msia.16. http://www.numdam.org/articles/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] The Jacobi stochastic volatility model, Finance Stoch., Volume 22 (2018), pp. 667-700 | DOI | MR | Zbl
[6] 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] 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] Jacobi Stochastic Volatility factor for the Libor Market Model (2020) (https://hal.archives-ouvertes.fr/hal-02468583)
[9] Générateurs de scénarios économiques : points d’attention et bonnes pratiques (2020) (acpr.banque-france.fr)
[10] 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] Rising interest rates, lapse risk, and the stability of life insurers (2017) (Technical report)
[12] Implémentation et calibrage d’un Générateur de Scénarios Economiques: impact sur la volatilité du Solvency Capital Requirement (2016) (Mémoire, EURIA)
[13] Market-Consistent valuation: a step towards calculation stability (2019)
[14] Interest rate models-theory and practice: with smile, inflation and credit, Springer, 2007
[15] 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] Mathematical methods of statistics (PMS-9), 9, Princeton University Press, 1946 | DOI
[17] Polynomial processes and their applications to mathematical finance, Finance Stoch., Volume 16 (2012) no. 4, pp. 711-740 | DOI | MR | Zbl
[18] 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] 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] Delegated Acts, Official Journal of the European Union (2014)
[21] 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] LIBOR and swap market models and measures, Finance Stoch., Volume 1 (1997) no. 4, pp. 293-330 | DOI | Zbl
[23] Economic scenario generators: a practical guide (2016) (Technical report)
[24] 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] LIBOR Market Model with stochastic volatility, J. Ind. Manag. Optim., Volume 2 (2006) no. 2, pp. 199-227 | MR | Zbl
Cité par Sources :
