Modeling the risk of a policyholder run

Modeling the risk of a policyholder run

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Speaker(s): Tobias Huber (LMU Munich), Johannes Jaspersen (LMU Munich)

Extreme lapse rates can severely distort life insurers' liquidity and profitability. We develop a model based on extreme value theory to assess the risk of such a policyholder run and show its practicability by utilizing lapse rates sourced from the National Association of Insurance Commissioners. Additionally, we apply this nonparametric approach to European data and thereby reveal difficulties in European insurance regulation. Our findings are crucial to risk managers and regulators as we provide not only a model to assess high levels of termination rates but also address the appropriateness of Solvency II's mass lapse scenario.

There is a variety of academic papers and industry publications on the modeling of life insurance lapse behavior (e.g. Kuo et al., 2003; Eling and Kiesenbauer, 2013). However, the risk of a policyholder run has only been considered sparely so far. Furthermore, the already existing approaches are either only applicable to variable annuity policies or assume interest rate related surrender behavior.

This paper, in contrast, provides a model to assess the risk of very high lapse rates regardless of any product type. As extreme lapse rates are very rare, we face the problem of having many lapse data under normal circumstances but only a few high lapse rates. Therefore, we develop a model that takes into account lapse rates of other life insurers as well. We use a procedure which is based on extreme value theory and allows us to decompose the lapse rates' unknown distribution function into two parts. The first part exploits the empirical distribution function to model lapse rates below a "suitable chosen" threshold. The second part uses the generalized Pareto distribution to model the excesses over the chosen threshold (Balkema and de Haan, 1974; Pickands, 1975).

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