Catastrophe Risk and the Implied Volatility Smile

Abstract

Property-casualty insurers are exposed to rare but severe natural disasters. This article 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 the rest of the economy and exhibits a seasonal pattern due to hurricanes. We are able to link the insurance-specific tail risk component derived from options with the risk spread from catastrophe bonds and global economic losses caused by catastrophes. Our results provide an accurate, high-frequency calculation for catastrophe risk linking the traditional derivatives market with insurance-linked securities.The hurricane does not know the rate that was charged for the hurricane policy, so it's not going to respond to how much you charge. And if you charge an inadequate premium, you will get creamed over time. . I would like to thank two anonymous referees, 1 We define catastrophe risk as a specific and independent component of the overall tail risk to which companies are exposed. Thus, catastrophe risk is one of many potential sources of distress to a firm (here, the P&C insurer). We follow Froot's (2001) definition of catastrophe risk, which relates to all events linked to natural hazard (e.g., hurricanes, earthquakes, wind and ice storms, floods, etc.) causing financial losses. In theory, our definition expands to man-made disaster such as terrorist attacks. However, such events not only affect the P&C insurance industry but also the rest of the economy (see, e.g., Brounen and Derwall, 2010;Thomann, 2013). As our research design relies on identifying differences between insurers and the rest of the economy, man-made disaster can only have a marginal impact on our analysis. Therefore, the focus of this article is on natural disasters.

Seasonality in catastrophe bonds and market‐implied catastrophe arrival frequencies

“…For the property and casualty insurance industry, Ammar (2020) identifies seasonal changes in the implied volatility smile of insurance stock options. Generally, the slope of the implied volatility smile is much steeper for insurance stock options than for the whole economy.…”

“…However, outside of the hurricane season, the smile for insurance stock options becomes flatter than during the hurricane season. Ammar (2020) indicates that markets might demand more in‐the‐money and at‐the‐money options outside of the hurricane season because large drops in insurance stock prices are less likely.…”

Insurability of pandemic risks

“…To overcome this data constraint, we proxy the insurer claim experience by its stock returns which is possible only for a subset of publicly traded insurers. Presumably, high individual insurance company losses translate into negative returns (Ben Ammar, 2020;Thomann, 2013). High losses going along with negative capital market returns contribute to a positive covariance between losses and the capital market.…”

Catastrophe risk, reinsurance and securitized risk-transfer solutions: a review

“…The learning effect of Katrina on stock prices and capitalizing can explain the difference in short sellers' behavior between the two hurricanes. As out-of-the-money (OTM) put options of insurance stock can provide more effective protection against CAT events than in-the-money (ITM) put options, Ammar (2020) uses the absolute difference between OTM and ITM put options to measure tail risk and identify a CAT risk premium in the implied volatility smile. The CAT risk premium is 120 basis points and strongly correlates with risk spreads from CAT bonds.…”