Pricing of Catastrophe Risk and the Implied Volatility Smile

Property-casualty (P&C) insurers are exposed to rare but severe natural disasters. This paper analyzes the relation between catastrophe risk and the implied volatility smile of insurance stock options. We find that the slope is significantly steeper compared to non-financials and other financial institutions. We show that this effect has increased over time, suggesting a higher risk compensation for catastrophic events. We are able to link the insurance-specific tail risk component derived from options with the risk spread from catastrophe bonds. Our results provide an accurate, high-frequency calculation for catastrophe risk linking the traditional derivatives market with insurance-linked securities (ILS).