Pricing mortality CAT bonds using extreme value theory

Details

Supervisors

Barigou, Karim

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

This thesis prices a mortality catastrophe bond with and without extreme value theory once the COVID-19 pandemic enters the estimation data. The instrument keeps the structure of Vita Capital VI Series 2021-1, transposed to a Belgian working-age index built from Human Mortality Database data over 1959 to 2023. Mortality shocks are defined as positive deviations of the index from an expanding Lee-Carter baseline, their distribution is spliced from an empirical body and either a generalised Pareto tail or the Gaussian continuation of the classical Lee-Carter innovation, and the Wang transform carries the spliced law to the pricing measure under the product-measure framework of Tang and Yuan, with a Vasicek block supplying discounting and the floating coupon. A 2×2 design crossing the tail law with a pre-pandemic and a pandemic-inclusive data vintage isolates the pricing effect of the tail. Restricted to ages 15 to 74, the index registers the pandemic far more weakly than all-age death counts, so the loss layer must be restruck to the realised series, and the pre-pandemic tail is bounded below the attachment, leaving the 300 basis point issuance spread reproducible only under the pandemic-inclusive vintage at a moderate loading. Extreme value theory moves the par spread by −18 basis points under the pre-pandemic vintage and by +202 under the pandemic-inclusive one. The sign reversal shows that the pricing effect of the extreme-value modification is a property of the data regime rather than of the method, with the vintage deciding the regime and the threshold moving only the magnitude within it.