Pricing catastrophe swaps with default risk and stochastic interest rates

Abstract

Catastrophe (CAT) swaps are bilateral contracts through which CAT losses can be transferred between two counterparties. They do not require collateral upon initiation, making them default-risky, have an average maturity of 3 years and may use index triggers, which suggest the valuation model must incorporate interest rate risk and basis risk. This study improves upon the literature and develops a dynamic structural framework to value CAT swaps and to analyze the impacts of interest rate risk, counterparty default risk, basis risk, trigger type, and other critical parameters. We estimate CAT swap spreads by using Monte Carlo simulation, with the main results indicating that the influence of stochastic interest rates on one-year CAT swap spreads is indeterminate, but is significant on 3-year and 5-year contracts. Counterparty default risk lowers CAT swap spreads, and all estimated default risk premiums are positive and economically significant. CAT loss uncertainty impacts contracts with different triggers in different ways, and basis risk becomes more severe for one-year contracts and where the correlation between the loss index and the buyer's actual loss is low.