Two hybrid models for dependent death times of couple: a common shock approach

Abstract

We combine two recent credit risk models with the Marshall–Olkin setup to capture the dependence structure of bivariate survival functions. The main advantage of this approach is to handle fatal shock events in the dependence structure since these two credit risk models allow one to match the time of death of an individual with a catastrophe time event. We also provide a methodology for adding other sources of dependency to our approach. In such a setup, we derive the no-arbitrage prices of some common life insurance products for coupled lives. We demonstrate the performance of our method by investigating Sibuya's dependence function. Calibration is done on the data of joint life contracts from a Canadian company.