By Yang Shen, Michael Sherris, Yawei Wang & Jonathan Ziveyi

This paper presents a novel combo insurance product design consisting of a variable annuity contract embedded with guaranteed minimum income benefits and long-term care insurance. This combo product provides enhanced benefits when the policyholder is functionally disabled. The Hamiltonian Monte Carlo simulation technique is utilised for numerically valuing the combo product whose underlying fund is proportionally invested in multiple asset classes. Product features including the elimination period and the maximum benefit period, are examined, and we show that the elimination period and the maximum benefit period can effectively reduce the product premium. From the policyholder’s perspective, we quantify the extent to which the combo product costs less than purchasing stand-alone products separately. From the provider’s perspective, we investigate the solvency capital requirement for the combo product under Solvency II and show that the combo product requires less solvency capital per initial cash inflow than an long-term care annuity. We perform fee sensitivity tests on model parameters to reveal some insights regarding risk management from the provider’s perspective. We conduct a utility analysis to explore the importance of long-term care insurance protection and investing in risky assets post-retirement, and we find policyholder gains utility from the variable annuity component and long-term care insurance component in the combo product design.

Source SSRN