Lapse risk in life insurance: correlation and contagion effects among policyholders' behaviors
Résumé
The present paper extends the existing literature on lapse risk by presenting a flexible way to model the lapse decisions in a life insurance portfolio. Correlation and contagion effects among policyholders are embedded in the modeling and risk margins estimates can be easily obtained under both stable regimes and stress scenarios. The proposed approach integrates the effects of policyholders' behaviors through the definition of a mathematical framework where the lapse intensity follows a dynamic contagion process: an external component, the shot-noise intensity, is added to the Hawkes-based one. Contrary to previous works, our shot-noise intensity is not constant and the resulting intensity process is not Markovian. We study the influence of the interest rates dynamics on policyholders' behaviors and the resulting impact on lapse risk margins. Closed-form expressions for the moments of the lapse intensity are provided, showing how the lapse risk is affected by massive copycat behaviors. A sensitivity analysis studies the lapse risk metrics as function of the model's parameters, while a simulation study compares our results with the ones obtained using standard practices. The numerical outputs highlight a potential strong misestimation of lapses under extreme scenarios with classical stress testing methodologies.
Origine : Fichiers produits par l'(les) auteur(s)