关键词: 巨灾互换, 可保性边界, Gerber-Shiu函数, 台风

Abstract: Climate change and increasingly extreme weather events, have caused a surge in natural disasters over the past 50 years. The insurance industry must play a more critical role in combating the climate crisis andimproving sustainability. China experiences several large natural disasters every year. How to develop China’s insurance market, expand underwriting coverage and enhance China’s overall insurance underwriting level has become one of China’s primary tasks.
As a new type of catastrophe derivatives, catastrophe swap has more simple transaction process, lower cost and greater flexibility, and can spread risks more effectively than those traditional catastrophe derivatives like catastrophe bond. At present, many international insurance companies are using catastrophe swaps as one of their main instruments of spreading risks. China has not yet carried out such products for the time being, and from successful international experience, it can be foreseen that, there is a great potential market in China for catastrophe swap. Due to the opacity of the transaction data, there are few researches on catastrophe swaps abroad, and even less domestically. Although there has been some progress in the design and pricing of catastrophe swaps, there is limited research on the application of these derivatives, which has caused insurance companies tobe lack of the basis for making the best decisions.
In order to enrich the research on the pricing theory and practical application of catastrophe swap in China, this paper explores the impact of a catastrophe swap, a new catastrophe derivative, on catastrophe risk insurability boundaries. The pricing model of the catastrophe swap under the assumption of continuous payment is given, and the surplus process of insurance companies under the catastrophe swap is obtained. By using Gerber-Shiu function, the ruin probability and insurability boundary functions of insurance companies in the state of participating or not participating in catastrophe swaps are derived. It is indicated that the limit of insurability for insurance companies to bear catastrophe risk is a function of the initial capital, loss settlement ratio, safety load factor, and maximum ruin probability. Based on this, this paper takes the TyphoonHato as a pricing example for catastrophe swaps using typhoon loss data from Guangdong Province in China. This study calculates the fair price difference of catastrophe swap, discusses the impact of catastrophic swaps on the insurability boundary, and further analyzes the relationship between the loss compensation proportion and initial capital, safety load coefficient and bankruptcy probability. The sensitivity analysis shows that the lower the initial capital of an insurance company, the greater the required safety load factor. On the contrary, the higher the initial cost, the lower the safety load factor. The proportion of loss compensation increases with the increase of initial capital and safety load factor. As the maximum bankruptcy probability that insurance companies can bear increases, the compensation ratio also significantly increases. The study confirms that participating in catastrophic swaps can help insurance companies expand the insurability boundary of catastrophic risks to a certain extent and improve underwriting capacity with unchanged initial capital, safety load factor, and maximum bankruptcy probability.
This paper provides some inspiration and reference for the research and application of catastrophic swaps in China. Given the particularity and complexity of catastrophic risk, there is still a lot of valuable research in the field of catastrophic swaps that needs to be further explored. More accurate characterization of catastrophic features and the design of catastrophic swaps that better meet the needs of the Chinese insurance market are the main tasks for further research.

Key words: catastrophe swap, boundary of insurability, Gerber-Shiu function, typhoon