基于损失比例的一类巨灾债券定价

Pricing a Class of Catastrophe Bond Based on Loss Ratio

摘要:

传统保险市场难以应对由于巨灾带来的巨额索赔，而保险公司可以通过发行巨灾债券，从而将部分巨灾风险转移至资本市场以达到分散索赔压力的目的。考虑一类按损失程度支付的巨灾债券定价问题，利用非齐次复合泊松分布作为巨灾累计损失分布，得到了票息支付过程和到期本金的支付比例，并且得到了风险中性下巨灾债券定价问题的表达式，最后对结果进行了数值模拟分析。结果表明预设的触发索赔门限值越高，触发概率越小，同时支付比例越小，但是巨灾债券贴现价值越大。

Abstract:

The traditional insurance market finds it difficult to cover the loss caused by massive claims resulting from catastrophe. Insurance companies can issue catastrophe bonds to transfer part of the catastrophe risk to the capital market thereby alleviating claims pressure through risk diversification. This paper considers the pricing of a class of catastrophe bond that makes payments based on the degree of loss. Using a nonhomogeneous compound Poisson distribution to model the cumulative catastrophic losses， it derives the coupon payment process and the proportion of principal repaid at maturity. It obtains an expression for the catastrophe bond pricing under the risk-neutral measure， and conducts numerical simulations to analyze the results. The findings show that the higher the preset loss threshold for triggering claims， the lower the probability of triggering and the smaller the payment ratio. However， the discounted value of the catastrophe bond increases..