Reinsurance strategy and network contagion: a macroprudential perspective

ABSTRACT

This article develops a network-based contagion model to investigate reinsurance strategy from a macroprudential perspective. We analyse the impact of reinsurance strategy on the spillovers from insurance sector to other economic sectors when a catastrophe such as a series of coronavirus-related claims occurs. The risk diversification level of the reinsurance strategy shows nonmonotonic effects on risk spillovers. When the diversified level is high enough relative to the actual magnitude of catastrophe, the spillover effect will not occur. However, when not sufficiently diversified, spillover effect is unavoidable and the diversified level shows a U-shaped relation with economic losses caused by risk spillovers. Our results thus reveal a new reinsurance insight for policymakers and regulators to develop macroprudential policy for managing systemic risk.

KEYWORDS:

• Spillover effect
• reinsurance network
• macroprudential regulation
• catastrophe

JEL CLASSIFICATION:

• D85
• G18
• G22

Disclosure statement

There was no potential conflict of interest related to the research described in this article.

Supplementary material

Supplemental data for this article can be accessed here.

Notes

¹ Lloyd’s of London told CNBC on 14 May 2020 about the impact of COVID-19 on insurance market, which can be found on the CNBC website.

² For a practical example, the government-ordered shutdowns during this pandemic crisis has caused great losses to America businesses. Since most businesses purchase business interruption insurance, the entire property insurance industry will be severely damaged or even bankrupted if business interruption policies cover COVID-19 related losses. On the contrary, if insurers deny the claims, their insureds’ businesses will likely to go bankrupt. In all cases, the economy will suffer a severe hit. See, for example, French (2020).

³ Subramanian and Wang (2018) indicate that catastrophe risks are generally be diversified by reinsurance.

⁴ The LMX Spiral is a phenomenon based upon excess of loss reinsurance contracts (primarily for property catastrophes) that developed within the London reinsurance market of the 1980s.

⁵ This is a systemwide perspective, in stark contrast to microprudential perspective which focus on individual institution, see, e.g. Freixas, Laeven, and Peydró (2015).

⁶ See, e.g. Buckham, Wahl, and Rose (2011), they state that the catastrophe is a major reason for insurers’ failure.

⁷ A ring-network $\mathbf{Y}=\{y_{ij}\}$ represents a configuration in which $y_{i,i+1}=y_{n,1}=y$ for any $i\in \mathcal{N}\mathrm{\setminus }\{n\}$, otherwise $y_{ij}=0$.

⁸ The number $e$ is a mathematical constant approximately equal to 2.71828.

⁹ The result that the economic losses with respect to diversified level shows a U-shaped relation still holds for complete networks. The proof is provided in Appendix A.7.

¹⁰ Out-degree is defined by $d={\sum }_{j\ne i}{1}_{\{y_{ij}>0\}}$.

¹¹ Such networks are generally called scale-free networks, in which some firms have many connections while others have few. It is a common configuration in the real-world economy, see Soramäki et al. (2007).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under [Grant number 71671094].