Modeling pandemic mortality risk and its application to mortality-linked security pricing

•We propose a mortality model that depicts the relevant pandemic effects using a threshold jump approach.•We consider mortality jumps related to the pandemic shock and to a specific country shock to capture pandemic mortality risks.•Pandemic jump occurs only when a pandemic event causes significant deaths worldwide.•We analyze the effect of pandemic mortality risk on pricing a mortality-linked bond using the first Swiss Re mortality bond. To provide insights for how to deal with pandemic mortality risk, this article introduces a mortality model that depicts the relevant pandemic effects on pricing mortality-linked securities, using a threshold jump approach. That is, to capture pandemic mortality dynamics across countries, we consider mortality jumps related to the pandemic shock and to a specific country shock. Pandemic jump occurs only when a pandemic event causes significant deaths worldwide, such as 1918 Spanish flu or COVID-19. Then the proposed pandemic mortality model can be adjusted according to country-specific mortality experiences. We further analyze the effect of pandemic mortality risk on pricing a mortality-linked bond. Using the first Swiss Re mortality bond as an example, a further derivation obtains the closed-form solution for the fixed-coupon mortality-linked bond in the pandemic mortality framework. Finally, this study details the impacts of pandemic mortality risk numerically by fitting the model to the United States, England and Wales, France, Italy, and Switzerland and calculating the fair spread of the mortality-linked bond.