Pricing zero-coupon CAT bonds using the enlargement of ltration theory: a general framework

TL;DR

This paper introduces a general mathematical framework using enlargement of filtration theory to price zero-coupon CAT bonds, accommodating different trigger event timings and providing closed-form pricing formulas.

Contribution

It develops a novel, more general model for CAT bond pricing that includes both accessible and inaccessible trigger event times, with explicit formulas and practical examples.

Findings

Closed-form pricing formulas for Model 2

More general than existing models in literature

Numerical example illustrating the pricing method

Abstract

The main goal of this paper is to use the enlargement of ltration framework for pricing zerocoupon CAT bonds. For this purpose, we develop two models where the trigger event time is perfectly covered by an increasing sequence of stopping times with respect to a reference ltration. Hence, depending on the nature of these stopping times the trigger event time can be either accessible or totally inaccessible. When some of these stopping times are not predictable, the trigger event time is totally inaccessible, and very nice mathematical computations can be derived. When the stopping times are predictable, the trigger event time is accessible, and this case would be a meaningful choice for Model 1 from a practical point of view since features like seasonality are already captured by some quantities such as the stochastic intensity of the Poisson process. We compute the main tools for pricing the zero-coupon CAT bond and show that our constructions are more general than some existing models in the literature. We obtain some closed-form prices of zero-coupon CAT bonds in Model 2 so we give a numerical illustrative example for this latter.