Research On Pricing Multiple Event Triggered Catastrophe Bonds Based On The Copula Function

There are many types of natural disasters,and the frequency of mega-disasters has increased year by year in recent years.China is one of the countries affected severely by natural disasters,and the direct economic losses caused by them are huge.However,nowadays China's assistance in the aftermath of a catastrophe still relies on government financial appropriations and social donations.The general insurance has a lower solvency and a narrower coverage,which cannot meet the huge relief needs after the catastrophe.In addition,due to the unpredictable occurrence of catastrophe risk events and huge economic losses,the traditional single-event-triggered catastrophe risk bonds have extremely high requirements on the insurance company's solvency,which is difficult to meet the various needs of the insurance market.Compared with single-event-triggered catastrophe risk bonds,a multi-event-triggered catastrophe risk bond will be less likely to be triggered and the investment risk will be smaller,so it will be easier for investors to accept and facilitate its implementation in the market.Based on China's national conditions,in order to design catastrophe risk bonds suitable for our country,this article used China's flood disasters as the research subject to conduct catastrophe risk bond pricing research,selected domestic flood data from 2004-2016,and used catastrophe economic losses and affected area and the number of catastrophe deaths as triggering conditions.Based on the ternary Copula function,the joint distribution of catastrophe risk was fitted,the inter-bank offered rate of Shanghai Banks was selected to replace the instantaneous interest rate,and the CIR interest rate model was adopted to price the multi-event catastrophe risk bonds.Based on the researches on catastrophe risk bonds at home and abroad,this paper studied the pricing of catastrophe risk bonds in China,innovated and optimized catastrophe loss fitting,and expanded the double-event trigger mechanism to multi-event trigger mechanism by using mixed Copula function.The pricing of catastrophe risk bonds mainly includes three steps: the fitting of catastrophe losses,the determination of interest rate term structure,and the establishment of pricing model.This article regarded economic losses,the death toll,and the affected area as the trigger condition to analyze its marginal distribution and fit for weibull distribution,logarithmic normal distribution andexponential distribution,and constructed a joint Clayton Copula between the two of the trigger conditions.Later,the idea of mixed Copula function was proposed to construct the ternary Copula function and perform parameter estimation,and then extended it to the multivariate case.After the loss fit distribution was obtained and the term structure of interest rates was determined,in this paper the CIR interest rate model was used to obtain the zero-coupon bond price,and the principal agent pricing model was used to determine the catastrophe risk bond price in the end.The empirical results showed that the price of a variety of flood bonds with different trigger conditions is analyzed and compared.The price of catastrophe risk bonds increases with the number of trigger events.The price of three event trigger catastrophe risk bonds is higher than that of double event trigger bonds.Double event triggered bond prices are higher than single event triggered bonds price.Because the investment risk triggered by multiple events is smaller,it is more conducive to its development in the future insurance market.