School of Mathematical Sciences, University of Electronic Science and Technology of China; Key Laboratory for Neuroinformation of Ministry Education, University of Electronic Science and Technology of China

In this paper, we present an approach of changing probability
measures associated with numeraire changes to the pricing of catastrophe event (CAT) derivatives.
We assume that the underlying asset and a discounted zero-coupon bond follow
a stochastic process, respectively. We obtain explicit closed form formulae that permit
the interest rate to be random. We shall see that sometimes it is convenient to change
the numeraire because of modeling considerations as well. Furthermore, we show that,
for compound Poisson losses, sometimes a continuum of jump sizes can be replaced by
finitely many jump sizes. Therefore, sometimes we can explore further applications of
the closed-form formulae beyond the case that the compound Poisson losses are finitely
many jump sizes. Finally, numerical experiments demonstrate how financial risks and
catastrophic risks affect the price of double trigger put option.