A Hybridized Stochastic SIR-Vasicek Model in Evaluating a Pandemic Emergency Financing Facility

ABSTRACT

In the context of the present global health crisis, we examine the design and valuation of a pandemic emergency financing facility (PEFF) akin to a catastrophe (CAT) bond. While a CAT bond typically enables fund generation to the insurers and re-insurers after a disaster happens, a PEFF or pandemic bond's payout is linked to random thresholds that keep evolving as the pandemic continues to unfold. The subtle difference in the timing and structure of the funding payout between the usual CAT bond and PEFF complicates the valuation of the latter. We address this complication, and our analysis identifies certain aspects in the PEFF's design that must be simplified and strengthened so that this financial instrument is able to serve the intent of its original creation. An extension of the compartmentalized deterministic epidemic model-which describes the random number of people in three classes susceptible (S), infected (I), and removed (R) or SIR for short-to its stochastic analog is put forward. At time t, S(t), I(t), and R (t) satisfy a system of interacting stochastic differential equations in our extended framework. The payout is triggered when the number of infected people exceeds a predetermined threshold. A CAT-bond pricing setup is developed with the Vasicek-based financial risk factor correlated with the SIR dynamics for the PEFF valuation. The probability of a pandemic occurrence during the bond's term to maturity is calculated via a Poisson process. Our sensitivity analyses reveal that the SIR's disease transmission and recovery rates, as well as the interest rate's mean-reverting level, have a substantial effect on the bond price. Our proposed synthesized model was tested and validated using a Canadian COVID-19 dataset during the early development of the pandemic. We illustrate that the PEFF's payout could occur as early as seven weeks after the official declaration of the pandemic, and the deficiencies of the most recent PEFF sold by an international financial institution could be readily rectified.