Pricing CAT Bonds under Shocks

Over the past few decades, catastrophe (CAT) bonds have become a popular financial instrument for insurers and reinsurers to mitigate their catastrophic losses and for investors to diversify their investment portfolios. In this work, we employ the risk-neutral pricing approach to price a one-period CAT bond written on a CAT event. The arrival process of the CAT event is modeled by a Cox process, and the intensity process and the interest rate process are assumed to jointly follow an affine jump-diffusion model that incorporates systemically relevant shocks. In this way, there are three types of risks embedded in the CAT bond, namely systemic, systematic, and jump risks. The pricing task is accomplished by constructing an equivalent martingale measure that allows for proper market prices of risk. Finally, we employ a hybrid approach to obtain a semi-closed form formula for the bond valuation and we conduct a sensitivity analysis of the bond price against various risk factors.