Risk-neutral Pricing of Mortality-linked Securities under Correlated Interest and Mortality Rates

In pricing mortality-linked securities, it is commonly assumed, but rarely tested, that the interest rate and the mortality rate are mutually independent. As we have witnessed, the COVID-19 outbreak in 2020 created both a health shock (in the form of sudden surges in mortality rate) and a financial shock (in the form of sharp drops in interest rate) over the globe, which seriously challenges the validity of this independence assumption in a pandemic era like now. In this research, we propose a bivariate affine jump diffusion model to jointly fit the interest rate and mortality rate, allowing for both simultaneous dependent jumps and correlated diffusions. After establishing the risk-neutral pricing measure, we conduct intensive empirical studies and sensitivity analysis based on the most up-to-date U.S. interest rate and mortality data as well as real market deals of mortality catastrophe bonds. Our work sheds new insights on the pricing framework for mortality-linked securities underlain by dependent interest and mortality rates.