# A full and synthetic model for Asset-Liability Management in life insurance, and analysis of the SCR with the standard formula

## TL;DR

This paper introduces a comprehensive synthetic Asset-Liability Management model for life insurance that incorporates regulatory profit sharing, realistic crediting rates, and bond investments, and analyzes the impact of interest rate models on the SCR under regulatory shocks.

## Contribution

It presents a novel ALM model capturing key life insurance features, including profit sharing and cash flow matching, and evaluates the SCR with different interest rate models and shocks.

## Key findings

- Interest rate model choice significantly affects SCR after shocks.
- Matching cash flows reduces SCR variability.
- Regulatory shocks impact SCR differently under various interest rate scenarios.

## Abstract

The aim of this paper is to introduce a synthetic ALM model that catches the main specificity 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 the 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 recommandation of the EIOPA on the shocks. In both cases, we illustrate the importance of matching cash-flows and its impact on the SCR.