Valuing Catastrophe Bonds Involving Credit Risks

Jian Liu,Fenghua Wen,Jihong Xiao,Lizhao Yan

doi:10.1155/2014/563086

Abstract

Catastrophe bonds are the most important products in catastrophe risk securitization market. For the operating mechanism, CAT bonds may have a credit risk, so in this paper we consider the influence of the credit risk on CAT bonds pricing that is different from the other literature. We employ the Jarrow and Turnbull method to model the credit risks and get access to the general pricing formula using the Extreme Value Theory. Furthermore, we present an empirical pricing study of the Property Claim Services data, where the parameters in the loss function distribution are estimated by the MLE method and the default probabilities are deduced by the US financial market data. Then we get the catastrophe bonds value by the Monte Carlo method.

Highlights

The securitization of catastrophe risk springing up in the early 1990s has created a direct link between the insurance industry and capital market
This paper presents a pricing model of CAT bonds with credit risks and conducts an empirical analysis of the US catastrophe market data using the Extreme Value Theory, where the parameters in the loss function distribution are estimated by the maximum likelihood estimation (MLE) method and the default probabilities are deduced by the US financial market data
When a catastrophic event takes place and its loss is higher than the prespecified trigger, special purpose vehicle (SPV) will provide compensation, which is from the loss of CAT bonds investors, to the sponsor according to the contract

Summary

Introduction

The securitization of catastrophe risk springing up in the early 1990s has created a direct link between the insurance industry and capital market. Zimbidis et al [7] use Extreme Value Theory to get the numerical results of CAT bonds prices under stochastic interest rates in an incomplete market framework. Li et al [9] study a representative agent-pricing model of the multievent CAT bonds by the data of catastrophic insured property losses of typhoon in China. This paper presents a pricing model of CAT bonds with credit risks and conducts an empirical analysis of the US catastrophe market data using the Extreme Value Theory, where the parameters in the loss function distribution are estimated by the MLE method and the default probabilities are deduced by the US financial market data. Based on the theoretical pricing formula, we get the CAT bonds value by the Monte Carlo method

Operating Mechanism of CAT Bonds

Valuation Framework

Numerical Analysis

Conclusions