Pricing catastrophe bonds by an arbitrage approach

This paper develops a simple arbitrage approach to valuing insurance-linked securities, which accounts for catastrophic events and interest rate randomness, notwithstanding a framework of non-traded underlyings. It shows that holders of catastrophe bonds are in a short position on one-touch binary options based upon risk-tracking indexes that obey jump-diffusion processes. Using first-passage time distributions, this contribution provides a closed-form valuation expression in the context of pure crashes, while it resorts to numerical simulations in the case of mid-range catastrophes. Comparative statics results point out that the term structure of yield spreads of catastrophe bonds is hump-shaped as for corporate bonds.