A new option for mortality–interest rates

Abstract

AbstractWe propose a new type of mortality–interest option related to a new random variable, the force of mortality–interest denoted as , the addition of the force of mortality and the force of interest. We assume 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.