Pricing Catastrophe Swaps: A Contingent Claims Approach

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.