Tarification d’obligations catastrophes liées à la mortalité avec sauts corrélés entre mortalité et taux d’intérêt

Details

Supervisors

Barigou, Karim

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

enThis thesis develops a pricing framework for mortality-linked catastrophe bonds that accounts for the dependence between extreme excess mortality shocks and interest rate movements. The COVID-19 pandemic is the starting point: it triggered unprecedented excess mortality in Belgium (P-score of 17.5% in 2020) alongside extreme financial volatility, which directly challenges the standard assumption that mortality risk and market risk are independent. We build a bivariate affine jump-diffusion (AJD) model where the short rate r_t and excess mortality μ_t evolve jointly under the historical measure P. Their dependence runs through two channels: a Brownian correlation ρ₁ and a jump correlation ρ₂. The risk-neutral measure Q is constructed via Girsanov's theorem for the diffusion part and exponential tilting for the jumps, introducing five risk premia ζ = (γ₁, γ₂ ; κ₁, κ₂ ; χ). The model is calibrated on weekly Belgian data spanning the pre-COVID (2017–2019) and post-COVID (2017–2022) periods using a Metropolis-Hastings algorithm. The risk-neutral parameters are estimated by minimising the gap between theoretical prices and observed spreads on the Vita Capital IV bond. Three findings stand out. First, jump intensity λ increases by a factor of roughly 33 across periods — well above the factor of 4.4 reported for the United States — and jump correlation stays strongly negative and stable (ρ₂ ≈ −0.97), consistent with the systematic monetary easing response to health crises. Second, comparing calibration scenarios shows the concrete cost of underestimating the pandemic risk regime on investor-required premia. Third, sensitivity analysis shows that extreme mortality risk is essentially a catastrophe frequency risk: the premium χ dominates ζ with a price impact of 9.691 points, against less than 0.003 points for the diffusion premia.