  Within the context of the banking-related literature on contingent
convertible bonds, we comprehensively formalise the design and features of a
relatively new type of insurance-linked security, called a contingent
convertible catastrophe bond (CocoCat). We begin with a discussion of its
design and compare its relative merits to catastrophe bonds and
catastrophe-equity puts. Subsequently, we derive analytical valuation formulae
for index-linked CocoCats under the assumption of independence between natural
catastrophe and financial markets risks. We model natural catastrophe losses by
a time-inhomogeneous compound Poisson process, with the interest-rate process
governed by the Longstaff model. By using an exponential change of measure on
the loss process, as well as a Girsanov-like transformation to synthetically
remove the correlation between the share and interest-rate processes, we obtain
these analytical formulae. Using selected parameter values in line with earlier
research, we empirically analyse our valuation formulae for index-linked
CocoCats. An analysis of the results reveals that the CocoCat prices are most
sensitive to changing interest-rates, conversion fractions and the threshold
levels defining the trigger times.
