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

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.

Decomposition of Disaster Region using Earthquake Parameter and STDM Distance: Catastrophe Bond Pricing Single Period

“…The results of the analysis are in line with (Burnecki, Giuricich, and Palmowski [9]; Chao and Katina [10]; Tang and Yuan [40]).…”

“…The higher the coupon rate, the higher the price of disaster bonds, and vice versa. The results of the analysis are in line with [9,10,40]. iii.…”

“…Let 𝑀 be the ekstrim magnitude, which is known by the POT method, then the cumulative distribution function (CDF) can be approximated by GPD [10] with shape parameter 𝜅(𝜅 ∈ 𝕽), location scale 𝝃(𝝃 ∈ 𝕽) and scale parameter 𝜎(𝜎 > 0) defined as follows:…”

Catastrophe Bond Diversification Strategy Using Probabilistic–Possibilistic Bijective Transformation and Credibility Measures in Fuzzy Environment

“…However, the investor will receive the entire face value and the coupons if the triggering event does not occur until the maturity date. The triggers that can be used in a catastrophe bond include a single trigger using a loss [37][38][39][40][41][42], multiple triggers using the number of deaths and the losses from the disaster [10,43,44], a single-parametric trigger using the earthquake's magnitude [45,46], a hybrid trigger using the earthquake's magnitude and loss [47], and a double-parametric trigger using the depth and magnitude of the earthquake [13,48]. When triggering events occur, parametric triggers have an advantage over other triggers in terms of high transparency and quicker payment regulation.…”

“…The scenario of receiving a coupon in Equation ( 16) in this study is that investors will receive a coupon of 3RT if the earthquake occurs at a maturity of less than 5.4 SR. Investors will receive (3R(T − 1) + 2R) if the earthquake occurs within a magnitude of 5.4 SR to 5.8 SR at (T − 1), or the investor could lose all of their coupons if the earthquake is more than 6.2 SR in the first year. Based on this scenario, the probability of each possible coupon is presented in Equation (43).…”