  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.
