A new option for mortality–interest rates. Issue 2 (13th December 2022) - Lin, Tzuling; Tsai, Cary Chi‐Liang
Abstract: We propose a new type of mortality–interest option related to a new random variable, the force of mortality–interest denoted as μ * ${μ }^{* }$, the addition of the force of mortality and the force of interest. We assume μ * ${μ }^{* }$ 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.