Pricing Options with Physically Based Exercise and Random Maturity

Hurricane bonds are uniquely structured to comprise two exercise condi-tions: a physically based condition that the underlying hurricane makes landfall at a pre-specified location and a standard moneyness condition that they end in the money. As the time of landfall is uncertain, their maturities are also uniquely random. Thus extant loss-based catastrophe bond pricing models cannot be directly applied. We propose a novel solution at the nexus of physical science and finance by integrating hurricane risk modeling and option pricing modeling to produce a coupled and physically based hurricane bond pricing model. We apply this methodology to pricing parametric hurricane bonds, featuring a parametric trigger based on physical param-eters related to hurricane tracks, radius, and intensity, as they have become increas-ingly popular in hurricane risk management. As hurricane arrival is underpinned by the discrete, sporadic, and random arrival of hurricane-specific information, we im-plement hurricane risk modeling by Monte Carlo simulation in information time. Our physically based model has the potential advantage of being able to apply to direct hedges against hurricane intensity and size uncertainties at landfall.