Valuing Multirisk Catastrophe Reinsurance Based on the Cox–Ingersoll–Ross (CIR) Model

Wen Chao,Polinpapilinho Katina

doi:10.1155/2021/8818486

Wen Chao, Polinpapilinho Katina

Open Access

https://doi.org/10.1155/2021/8818486

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Abstract

Catastrophe risks lead to severe problems of insurance and reinsurance industry. In order to reduce the underwriting risk, the insurer would seek protection by transferring part of its risk exposure to the reinsurer. A framework for valuing multirisk catastrophe reinsurance under stochastic interest rates driven by the CIR model shall be discussed. To evaluate the distribution and the dependence of catastrophe variables, the Peaks over Threshold model and Copula function are used to measure them, respectively. Furthermore, the parameters of the valuing model are estimated and calibrated by using the Global Flood Date provided by Dartmouth College from 2000 to 2016. Finally, the value of catastrophe reinsurance is derived and a sensitivity analysis of how stochastic interest rates and catastrophe dependence affect the values is performed via Monte Carlo simulations. The results obtained show that the catastrophe reinsurance value is the inverse relation between initial value of interest rate and average interest rate in the long run. Additionally, a high level of dependence between catastrophe variables increases the catastrophe reinsurance value. The findings of this paper may be interesting to (re)insurance companies and other financial institutions that want to transfer catastrophic risks.

Highlights

Nowadays, catastrophe events, such as floods, earthquakes, hurricanes, storms, and man-made disasters claiming many lives and causing great property loss, are of low-probability but relatively great destructiveness
We apply the Cox–Ingersoll–Ross (CIR) model to depict the characteristics of interest rates market, thereby providing more accurate value of catastrophe reinsurance contract
In the study of catastrophe reinsurance, we focus our attention on the effect of interest rate on the reinsurance values

Summary

Introduction

Catastrophe events, such as floods, earthquakes, hurricanes, storms, and man-made disasters claiming many lives and causing great property loss, are of low-probability but relatively great destructiveness. E early valuing model is due to Strickler [1] (see [2]), in which a constant deterministic rate of catastrophes is assumed, and it is limited to catastrophes claiming at most 1500 lives. To overcome these shortcomings of the valuing model used in [1], Ekheden and Hossjer [3] established a new model based on compound Poisson process to value the catastrophe excess of loss cover Another common technique applied to value reinsurance contracts is based on simulation approach; for example, see [4,5,6,7] and the references therein. We apply the Cox–Ingersoll–Ross (CIR) model to depict the characteristics of interest rates market, thereby providing more accurate value of catastrophe reinsurance contract. Where α > 0 is the speed of mean-reverting, μ > 0 is a mean of interest rate in the long run, β > 0 is the volatility of the interest rate, and W(t) is a standard Brownian process

Valuation Framework

Parameter Estimation of the Valuing Model

Numerical Example and Simulation

Sensitivity Analysis for the Catastrophe Reinsurance