Valuation of contingent convertible catastrophe bonds - the case for equity conversion

TL;DR

This paper develops analytical valuation models for index-linked contingent convertible catastrophe bonds (CocoCats), comparing their features to other catastrophe-linked securities and analyzing their sensitivity to key financial parameters.

Contribution

It provides the first comprehensive formalisation and analytical valuation formulae for CocoCats, including their design, features, and empirical analysis under specific market assumptions.

Findings

CocoCat prices are highly sensitive to interest rates, conversion fractions, and trigger thresholds.

The analytical models effectively capture the impact of market and catastrophe risks on CocoCat valuation.

CocoCats offer a novel insurance-linked security with distinct features compared to traditional catastrophe bonds.

Abstract

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.