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PRICING CATASTROPHE SWAPS A CONTINGENT CLAIMS APPROACH

Alexander Braun
Institute of Insurance Economics, University of St. Gallen,

Abstract

While catastrophe bonds, futures and options have attracted increasing scholarly attention through-
out the last two decades, the catastrophe swap, a financial instrument of growing importance for risk
managers and investors, has been virtually neglected altogether. This paper aims at filling the gap
by discussing key characteristics of common contracts, providing insights with regard to the current
state of the market and developing a parsimonious contingent claims pricing formula for catastrophe
swaps. We vindicate a risk-neutral valuation approach and, in the absence of market quotes for an
empirical verification, decide to emphasize tractability at the expense of jumps in the dynamics of
the underlying index. The resulting catastrophe swap spread increases for lower attachment levels, a
higher loss index volatility as well as rising interest rates and the model encompasses the flexibility
to generate upward-sloping or hump-shaped term structures. In addition, numerical analyses reveal
that the inclusion of a jump component in the loss index dynamics can have a substantial impact on
the magnitude of the cat swap spread and the level of the term structure. However, it is also shown
that for the short maturities currently traded a term structure of implied volatilities exists, for which
the proposed closed-form solution exactly matches the results of the jump-diffusion case.

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