Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors

The present paper proposes a new methodology to model the lapse risk in life insurance by integrating the dynamic aspects of policyholders’ behaviors and the dependency of the lapse intensity on macroeconomic conditions. Our approach, suitable to stable economic regimes as well as stress scenarios, introduces a mathematical framework where the lapse intensity follows a dynamic contagion process, see Dassios and Zhao (2011). This allows to capture both contagion and correlation potentially arising among insureds’ behaviors. In this framework, an external market driven jump component drives the lapse intensity process depending on the interest rate trajectory: when the spread between the market interest rates and the contractual crediting rate crosses a given threshold, the insurer is likely to experience more surrenders. A log-normal dynamic for the forward rates is introduced to build trajectories of an observable market variable and mimic the effect of a macroeconomic triggering event based on interest rates on the lapse intensity. Contrary to previous works, our shot-noise intensity is not constant and the resulting intensity process is not Markovian. Closed-form expressions and analytic sensitivities for the moments of the lapse intensity are provided, showing how lapses can be affected by massive copycat behaviors. Further analyses are then conducted to illustrate how the mean risk varies depending on the model’s parameters, while a simulation study compares our results with those obtained using standard practices. The numerical outputs highlight a potential misestimation of the expected number of lapses under extreme scenarios when using classical stress testing methodologies.