Calibrating Cat Bonds for Mexican Earthquakes
Härdle, Wolfgang Karl, Cabrera, Brenda López, Journal of Risk and Insurance
This article examines the calibration of a real parametric catastrophe bond (CAT bond) for earthquakes sponsored by the Mexican government, which is of a high interest as it delivers several policy-relevant findings. The results demonstrate that a combination of reinsurance and CAT bond is optimal in the sense that it provides coverage for a lower cost and lower exposure at default than reinsurance itself. A hybrid CAT bond for earthquakes is also priced in order to reduce the basis and moral risk borne by the sponsor and to reflect the value of the loss by several variables.
As a result of its geographical location, Mexico finds itself under threat from a great variety of natural phenomena that can cause disasters, such as earthquakes, volcanic eruptions, hurricanes, forest fires, floods, and aridity (dryness). In the event of a disaster, the effects on financial and natural resources are huge and volatile. Mexico's first priority is to transfer seismic risk, because although it is the less recurrent, it has the biggest impact on the population and the country. For example, an earthquake of magnitude 8.1Mui Richter scale, which hit Mexico in 1985, destroyed hundreds of buildings and caused thousands of deaths. After a natural disaster, reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. For insurers, reinsurers and other corporations, CAT bonds are hedging instruments that offer multiyear protection without the credit risk present in reinsurance by providing full collateral for the risk limits offered through the transaction. For investors, CAT bonds offer attractive returns and reduction of portfolio risk, since CAT bonds defaults are uncorrected to the defaults of other securities.
Baryshnikov, Mayo, and Taylor (2001) present an arbitrage-free solution to the pricing of CAT bonds under conditions of continous trading and according to the statistical characteristics of the dominant underlying processes. Also under an arbitrage-free framework, Vaugirard (2003) evaluates CAT bonds by Monte Carlo simulation methods and stochastic interest rates. Burnecki and Kukla (2003) and Burnecki, Hardie, and Weron (2005) correct and apply the results of Baryshnikov, Mayo, and Taylor to calculate nonarbitrage prices of a zero-coupon and coupon CAT bond. Lee and Yu (2002) develop a methodology that incorporates stochastic interest rates and more generic loss processes to price default-risky CAT bonds. They also analyze the value of the bond under the considerations of default risk, moral hazard, and basis risk. Instead of pricing, Anderson et al. (2000) provide benefits to CAT bonds by introducing an extensive relative value analysis. Cummins, Lalonde, and Phillips (2004) study the effectiveness of loss index securities in hedging catastrophic risk. Others, like Croson and Kunreuther (2000), focus on the CAT management and their combination with reinsurance. Lee and Yu (2007) examine how a reinsurance company can increase the value of a reinsurance contract and reduce its default risk by issuing CAT bonds. Barrieu and Loubergé (2009) point out that the downside risk aversion and ambiguity aversion have caused the limited success of CAT bonds; therefore, they propose to replace simple CAT bonds with hybrid CAT bonds, providing catastrophic risk transfer with protection against a stock crash to complete the market. Cummins and Weiss (2009) and Cummins and Trainar (2009) argue that securitization permits insurers and reinsurers to achieve optimal combination of diversification and shifting of catastrophic risk to the capital markets. The link between parametric/index CAT bonds and reinsurance has been investigated by Finken and Laux (2009), who complain that parametric or index CAT bonds provide low-risk insurers with an alternative to reinsurance contracts, leading to less cross-subsidization in the reinsurance market.
As the study of natural catastrophe models plays an important role in the prevention and mitigation of disasters, the main motivation of this article is the analysis of pricing CAT bonds. …