A synthetic model for asset-liability management in life insurance, and analysis of the SCR with the standard formula
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A synthetic model for asset‑liability management in life insurance, and analysis of the SCR with the standard formula Aurélien Alfonsi1,2 · Adel Cherchali1,2 · Jose Arturo Infante Acevedo3 Received: 19 September 2019 / Revised: 30 March 2020 / Accepted: 11 June 2020 © EAJ Association 2020
Abstract The aim of this paper is to introduce a synthetic ALM model that catches the key features of life insurance contracts. First, it keeps track of both market and book values to apply the regulatory profit sharing rule. Second, it introduces a determination of the crediting rate to policyholders that is close to practice and is a trade-off between the regulatory rate, a competitor rate and the available profits. Third, it considers an investment in bonds that enables to match a part of the cash outflow due to surrenders, while avoiding to store the trading history. We use this model to evaluate the Solvency Capital Requirement (SCR) with the standard formula, and show that the choice of the interest rate model is important to get a meaningful model after the regulatory shocks on the interest rate. We discuss the different values of the SCR modules first in a framework with moderate interest rates using the shocks of the present legislation, and then we consider a low interest framework with the latest recommendation of the EIOPA on the shocks. In both cases, we illustrate the importance of matching cash-flows and its impact on the SCR. Keywords ALM model · Solvency capital requirement · Standard formula · Cashflow matching · Liquidity gap · Surrender risk · Book value · Profit sharing
* Aurélien Alfonsi [email protected] Adel Cherchali [email protected] Jose Arturo Infante Acevedo [email protected] 1
CERMICS, Ecole des Ponts, Marne‑la‑Vallée, France
2
MathRisk, Inria, Paris, France
3
GIE AXA, 25 Avenue Matignon, 75008 Paris, France
13
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1 Introduction Life insurance contracts are very popular in the world and involve very large portfolios. In 2017, the life insurer assets were about 7.5 trillions of euros in Europe (source: Insurance Europe) and 7.2 trillions of dollars in the United States (source: American Council of Life Insurers). To manage these large portfolios on a long run, insurance companies perform what is called an Asset and Liability Management (ALM). We refer to the recent paper [1] for an overview of the current topics and issues of ALM. Basically, insurance companies invest the deposit of policyholders in different asset classes (equity, sovereign bonds, corporate bonds, real estate, ...), while respecting a performance warranty with a profit sharing mechanism for the policyholders. Thus, insurance companies have to determine an appropriate allocation between the different types of asset. This allocation should be a good trade-off between risk and returns, but also with the capital requirement imposed by the regulator to handle the portfolio. To determine a suitable allocation strategy, it is worthwhile to rely on an ALM model tha
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