双随机复合泊松损失下巨灾债券定价与数值模拟

Pricing Catastrophe Bonds under the Doubly Stochastic Compound Poisson Losses and Numerical Simulation

上世纪90年代出现的巨灾债券是以规避巨灾财产损失为目的的新型非传统风险转移金融创新工具之一,在我国有良好的发展前景。本文针对巨灾风险事件呈现出周期性与不规则的上升特征,构建了BDT过程用以刻画巨灾风险的抵达过程,并基于风险中性测度技术,在随机利率环境与双随机复合泊松损失条件下,导出了巨灾债券定价公式。进而结合伦敦同业银行拆借利率数据与美国保险服务所提供的PCS损失指数估计并校正了模型参数。最后,通过数值模拟检验了利率风险与巨灾风险如何影响巨灾债券的价格,同时验证了定价模型的可行性。

Due to an increasing risk of extreme losses caused by value concentration and climate change as well as due to a limited（and volatile）capacity of traditional reinsurance and retrocession markets.Against this background,Alternative risk transfer（ART）intends to provide additional（re）insurance coverage by transferring insurance risks to the capital market,which offers considerably higher capacities and can thus help satisfying the demand.catastrophe risk bonds are by far the most successful and importantART financial innovation,hence have large potential in China.Intergovernmental Panel on Climate Change（IPCC）（2013）projections of more frequent and more intense extreme weather events in the 21 st century and the occurrence and severity of abnormal climate change presents an irregular cycle with an upward trend.To capture the two catastrophic characteristics,a doubly stochastic Poisson process with Black DermanToy（BDT）intensity is proposed to model the arrival process for catastrophic risk events.The empirical results reveal the BDT arrival rate process is superior to the mean-reverting arrival process due to its larger E and d,and smaller RMSE,MAE and U.Second,to depict extreme features of catastrophic risks,the Block Maxima Method（BMM）in extreme value theory（EVT）is adopted to characterize the tail characteristics of catastrophic risk loss distribution.And then the loss distribution is analyzed and assessed using the graphics technology,the goodness-of-fit test,and model evaluation,it is found that the Generalized Extreme Value（GEV）distribution is the best fit.Furthermore,apricing formula is derived for catastrophe bonds in a stochastic interest rates environment with the losses following a compound doubly stochastic Poisson process using risk-neutralized measure method.Next,the parameters of the pricing model are estmated and calibrated using the catastrophe loss data provided by the Property Claim Services（PCS）Unit of the Insurance Service Office（ISO）from 1985 to 2010and 12-Month London Interbank Offered Rate（LIBOR）based on U.S.Dollar.Finally,simulation results verify our model predictions and demonstrate how financial risks and catastrophic risks affect the prices of catastrophe bonds.