Abstract
The Solvency II directive asks insurance companies to derive their solvency capital requirement from the full loss distribution over the coming year. While this is in general computationally infeasible in the life insurance business, an application of the Least-Squares Monte Carlo (LSMC) method offers a possibility to overcome this computational challenge. We outline in detail the challenges a life insurer faces, the theoretical basis of the LSMC method and the necessary steps on the way to a reliable proxy modeling in the life insurance business. Further, we illustrate the advantages of the LSMC approach via presenting (slightly disguised) real-world applications.
Highlights
The standards set out in the Solvency II directive mark the starting point for the recent developments of proxy modeling to calculate solvency capital requirements in the insurance sector, see European Parliament and European Council (2009)
We outline in detail the challenges a life insurer faces, the theoretical basis of the Least-Squares Monte Carlo (LSMC) method and the necessary steps on the way to a reliable proxy modeling in the life insurance business
Among them are sophisticated techniques such as Least-Squares Monte Carlo (LSMC), which we focus on in this paper
Summary
The standards set out in the Solvency II directive mark the starting point for the recent developments of proxy modeling to calculate solvency capital requirements in the insurance sector, see European Parliament and European Council (2009). In more complex business regulations, such as in Germany, the company has to assure it will have enough assets to cover the expected annuity payments during the entire lifetime of the policy Each year it has to set aside a sufficient provision for the future benefits taking into account the interest rate guarantees promised to the customer. The main purpose of this paper is to give a current snapshot of why and how the companies in the life insurance sector can use an LSMC-based approach to derive their full loss probability distribution forecasts. Even though we do not have the intention of giving a step-by-step worked example, we offer numerical illustrations in which we place our focus on the proxy function calibration, validation and evaluation and compare LSMC to the directly calculated full loss distribution (nested stochastics).
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