A new option for mortality–interest rates

Abstract

We propose a new type of mortality-interest option related to a new random variable, the force of mortality-interest denoted as μ*, the addition of the force of mortality and the force of interest. We assume μ* moves approximately linearly, design the new mortality-interest option, and then derive closed-form formulas for its expected values. We show that using the new mortality-interest options, an annuity provider and a life insurer can, respectively, hedge the longevity and mortality risks with interest rate risk; a financial intermediary selling the new options can benefit from natural hedges resulted from two-side businesses with the annuity provider and life insurer.