From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital

In this paper we raise the matter of considering a stochastic modeling of the surrender rate instead of the classical S-shaped deterministic curve (in function of the spread), still used in almost all insurance companies. A stochastic model in which surrenders are conditionally independent with respect to a S-curve disturbance would be tempting in some extreme scenarii, especially to address the question of the lack of data. However, we explain why this conditional independence between policyholders, which has the advantage to be the simplest assumption, looks particularly maladaptive when the spread increases. Indeed the correlation between policyholders’ decisions is most likely to increase in this situation. We suggest and develop a simple model which integrates those phenomena. With stochastic orders it is possible to compare it to the conditional independence approach qualitatively. In an partially internal Solvency II model, we quantify the impact of the correlation phenomenon on a real life portfolio for a global risk management strategy. Surrender risk, also called lapse risk represents one of the main dangers faced by a life insurance institution. It corresponds to the risk that many policyholders surrender their contract earlier than expected and choose to reinvest ∗ Corresponding author Email addresses: [email protected] (Stéphane Loisel), [email protected] (Xavier Milhaud). Preprint submitted to European Journal of Operational Research July 7, 2010 ha l-0 05 02 84 7, v er si on 1 15 J ul 2 01 0 Author manuscript, published in "European Journal of Operational Research 214, 2 (2011) 348-357"