Valuing catastrophe bonds involving correlation and CIR interest rate model

Analysis of Risk Premium Determinants on Cat Bonds

Insurance securitization has long been hailed as an important tool to increase the underwriting capacity for companies exposed to catastrophe-related risks. However, global volumes of insurance securitization have remained surprisingly low to date which raises questions over its benefits. In this paper, we examine changes in the market value of insurance and reinsurance firms which announce their engagement in insurance securitization by issuing catastrophe (Cat) bonds. Consistent with the hitherto underwhelming contribution of Cat bonds to global catastrophe coverage, we do not find evidence that Cat bonds lead to strong wealth gains for shareholders in the issuing firm. More importantly, we report large variations in the distribution of wealth effects in response to the issue announcement. We show that the wealth effects for shareholders in firms which issue Cat bonds appear to be driven by explanations according to which Cat bonds offer cost savings relative to other forms of catastrophe risk management (and less by the potential of Cat bonds to hedge catastrophe risk). Thus, abnormal returns are particularly large for issues by firms which face low levels of loss uncertainty (which reduces the information acquisition costs in financial markets) as well as for issues during periods when prices for catastrophe coverage (including Cat bonds) are low.

Disasters have significant environmental, human, social, economic, and financial impacts. These effects are potentially long-lasting and have multi-generational consequences. Due to climate change, disasters have cascading and compound effects, heightening the financial risks. However, the number of countries issuing CAT Bonds as a financial instrument for tackling the financial burden of disasters is less than 5% as of 2023. This study explores the need to use CAT Bonds as a risk transfer mechanism that allows governments and insurers to spread their climate change risk across capital markets. It presents a comprehensive cross-country level analysis of the potential drivers that influence the CAT bond issuance at a sovereign level for 131 countries from 2016 to 2021 to understand their significance for issuers and non-issuers of CAT Bonds. These potential drivers were filtered after an exploratory factor analysis. Nonetheless, the imbalance between the number of issuers and non-issuers has resulted in poor classification accuracy results and bias. Hence, this study employs Logistic Regression with Synthetic Minority Over-sampling Technique (SMOTE) and without SMOTE. Further, a comparison study between the effective CAT Bond issuance in the Philippines against non-issuance in India was conducted to determine the obstacles in the Indian setting. The result from the study indicates that a country’s exposure to hazards, population growth, investment freedom, regulatory quality, gross budget balance, stock traded and rule of law have statistically significant impact on the issue of CAT Bond. Highlighting the Indian context, the major challenges the country faces in issuing CAT Bonds are its stringent rule of law, regulatory inferiority, economic uncertainty, and less stock traded.

To encourage further development of catastrophe (cat) bond, understanding the causes of cat bond premium puzzle is necessitated. Considering the property of entropy to measure uncertainty, this paper establishes an entropy model about risk assessment in catastrophe bond investors' decision making. Moreover, this article analyzes the model and compares relative influence through simulating actual behavior of both rational and non-rational investors. The conclusions obtained show that with inadequate information, cognitive biases and collecting cost increase the high yield demand of investors in cat bond market.

Catastrophe bonds are financial instruments, which enable to transfer the natural catastrophe risk to financial markets. This paper is a continuation of our earlier research concerning catastrophe bond pricing. We assume the absence of arbitrage and neutral attitude of investors toward catastrophe risk. The interest rate behavior is described by the two-factor Vasicek model. To illustrate and analyze obtained results, we conduct Monte Carlo simulations, using parameters fitted for real data on natural catastrophes. Besides the crisp cat bond pricing formulas, we obtain their fuzzy counterparts, taking into account the uncertainty on the market. Moreover, we propose an automated approach for decision making in fuzzy environment with relevant examples presenting this method.

The study of natural catastrophe models plays an important role in the prevention and mitigation of disasters. After the occurrence of a natural disaster, the reconstruction can be financed with catastrophe bonds (CAT bonds) or reinsurance. This paper examines the calibration of a real parametric CAT bond for earthquakes that was sponsored by the Mexican government, which is based on the estimation of the intensity rate of the arrival process of earthquake (which would trigger this particular CAT bond) from the two sides of the contract: the reinsurance and the capital markets. Additionally, the intensity rate from the historical data was estimated to conduct a comparative analysis. The results demonstrate that, under specific conditions, the financial strategy of the government, a mix of reinsurance and CAT bond, is optimal in the sense that it provides coverage of USD 450 million for a lower cost than the reinsurance itself. <italic>JEL Classification: G19, G29, N26, N56, Q29, Q54</italic>

Risk-based catastrophe bond design for a spatially distributed portfolio

Financial Adaptation to Climate Change via Public Interest Weather Derivatives and Catastrophe Bonds in the Wake of the Financial Meltdown

The scale of wildfires, in terms of acreage burned and mortality rates, is risingdue to climate change. There are various causes for wildfire ignition; however, power lines are one of the most significant factors, leading to some of the most devastating wildfire events over the past decade and even bankrupting electric utilities. Traditional insurance strategies are often not applicable for providing financial resilience to electric utilities against such catastrophic events. This paper quantifies the associated risk and proposes a catastrophe bond (CAT bond) as a form of parametric insurance to cover a portion of the risk. Vegetative fuel, weather, power grid, and historical wildfire ignition data are integrated into a proposed simulation-based methodology to accurately price the risk of the third-party wildfire liability, transmission line reconstruction, and the cost of load-shedding. The proposed methodology offers a useful tool for transmission system owners to transfer a portion of the risk of wildfire ignition to CAT bond investors. In addition, the premium calculation is analyzed through a sensitivity analysis to calibrate the indemnity-based CAT bond parameters.

Reinsurance and CAT bonds are two alternative risk management instruments used by insurance companies. Insurers should be indifferent between the two instruments in a perfect capital market. However, the theoretical literature suggests that insured risk characteristics and market imperfections may influence the effectiveness and efficiency of reinsurance relative to CAT bonds. CAT bonds may add value to insurers’ risk management strategies and may therefore substitute for reinsurance. Our study is the first to empirically analyse if and under what circumstances CAT bonds can substitute for traditional reinsurance. Our analysis of a comprehensive data set comprising U.S. P&C insurers’ financial statements and CAT bond use shows that insurance companies’ choice of risk management instruments is not arbitrary. We find that the added value of CAT bonds mainly stems from non-indemnity bonds and reveal that (non-indemnity) CAT bonds are valuable under high reinsurer default risk, low basis risk and in high-risk layers.

This article develops a contingent claim model to price a default-risky, catastrophe-linked bond. This model incorporates stochastic interest rates and more generic loss processes and allows for practical considerations of moral hazard, basis risk, and default risk. The authors compute default-free and default-risky CAT prices by using the Monte Carlo method. The results show that both moral hazard and basis risk drive down the prices substantially; these effects should not be ignored in pricing the CAT bonds. The authors also show how the prices are related to catastrophe occurrence intensity, loss volatility, trigger level, the issuing firm's capital position, debt structure, and interest rate uncertainty. INTRODUCTION Property-liability insurance companies traditionally hedge their low-loss frequency, high-loss-severity catastrophe risks by buying catastrophe reinsurance contracts. The traditional reinsurance and catastrophe insurance options, which trade in the Chicago Board of Trade (CBOT), are asset hedge instruments for insurers' or reinsurers' catastrophe risk management. A recent innovation in catastrophe risk management is the catastrophe (CAT hereafter). The CAT which is also named as an Act of God bond or insurance-linked bond, is a liability hedge instrument for insurance companies, for which there have been many successful CAT issues recently. (1) CAT provisions have debt-forgiveness triggers whose generic design allows for the payment of interest and/or the return of principal forgiveness, and the extent of forgiveness can be total, partial, or scaled to the size of loss. Moreover, the debt forgiveness can be triggered by the insurer's (or reinsurer's) actual losses or on a compos ite index of insurers' losses during a specific period. The advantage of a CAT hedge for (re)insurers (insurers, hereafter) is that the issuer can avoid the credit risk that may arise with traditional reinsurance or catastrophe-linked options. The CAT bondholders provide the hedge to the insurer by forgiving existing debt. Thus, the value of this hedge is independent of the bondholders' assets, and the issuer has no risk of nondelivery on the hedge. However, from the bondholder's perspective, the default risk, the potential moral hazard behavior, and the basis risk of the issuing firm are critical in determining the value of CAT bonds. The moral hazard behavior occurs when the insurer's cost of loss control efforts exceeds the benefits from debt forgiveness. That is, the insurer has an incentive to pay the claims more generously when the loss amount is near the trigger set in the debt-forgiveness provision. Doherty (1997) pointed out that moral hazard results from less loss control efforts by the insurer issuing CAT bonds because these efforts will increase the amount of debt that must be repaid. Bantwal and Kunreuther (1999) also noted the tendency for insurers to write additional policies in a catastrophe-prone area, spending less time and money in their auditing of losses after a disaster. The moral hazard behavior may increase the claim payments at the expense of the bondholders' coupon (or principal) reduction and affect the price. Another important element that needs to be considered in pricing a CAT is the basis risk. The CAT bond's basis risk refers to the gap between the insurer's actual loss and the composite index of losses that prevents the insurer from receiving complete risk hedging. The basis risk may cause insurers to default on their debt in the case of high individual loss but low index of loss, and therefore affects the price. A tradeoff indeed exists between basis risk and moral hazard. If one uses an independently calculated index to define the CAT payments, then the insurer's opportunity to cheat the bondholders is reduced or eliminated, but basis risk is created. Doherty (1997) and Belonsky (1998), among others, have looked into the effect of basis risk and moral hazard, but not from the perspective of pricing. …

The article proposes a method for assessing the bilateral relationships between catastrophe and sovereign bonds to analyze financial risks within the framework of China’s global infrastructure initiative “Belt and Road”. Countries included in the China - EU land transport corridor have a high risk of natural disasters, which could negatively affect the infrastructure being created and local communities. Investments in infrastructure projects by China are often made subject to sovereign guarantees from partner countries. In case of natural disasters, the traditional use of state reserve funds is not always effective, since the insurance markets of the countries of the China - EU land transport corridor are dominated by protectionism, the indicator of which is the low level of import of insurance services. As a more effective tool for covering losses in the event of catastrophic threats to the infrastructure of the China - EU transport corridor, one can consider insurance derivatives (Insurance Linked Securities - ILS) and sovereign parametric catastrophe bonds, in particular. The article analyzes the relationship between catastrophe and sovereign bonds of a number of countries (China, Kazakhstan, Russia, Turkey). Based on the results of testing the hypothesis (H1), the dependence of the interest rate on sovereign bonds of Kazakhstan, China, Russia and Turkey on the interest rates on catastrophic bonds of the Swiss Re Cat Bonds Index was established. A complete inverse relationship between catastrophe bond rates and sovereign bond rates, in accordance with hypothesis (H2), was not revealed.

Out-of-Sample Performance of Spot Interest Rate Models

Climate change implications for the catastrophe bonds market: An empirical analysis

This paper presents an analysis of models for Japanese short-term inter- est rate. The models are constructed based on mean reverting model using Bayesian method to capture the dynamics of short-term interest rate. The parameters of our models are estimated by marginal likelihood and posterior expectation and we shall make model selection using the information criterion EIC(extended information cri- terion). An application of the models will be implemented using weekly Japanese average interest rates on certificates of deposit (new issues) less than 30 days in the period from January 2001 to December 2008. 1 Introduction Correct modeling of the short-term interest rate is essential in finace, as it is this rate that is fundamental to the pricing of securities and important for risk man- agement. In the study of the short-term interest rate dynamics, various models have been suggested. There are examples of these models, such as Vasicek model by Vasicek(1977), CIR model by Cox, Ingersoll and Ross(1985) and so on. An empirical comparison of these models was made by Chan, Karolyi, Longstaff and Sanders(1992). In the paper, the param- eters are estimated by generalized method of moments(GMM) and they implemented the hypothesis testing methods developed by Newey and West for evaluation of the models. In the parameter estimation of mean reverting model using GMM, it is known that the results are easy to be influenced by an initial values, and it becomes often unstable. Recently, Ahangarani(2005) employed maximum likelihood method for parameter esti- mation and log likelihood ratio test for model selection, and Kawada(2007) implemented GMM and made model selection using the information criterion EIC(extended information criterion) for various short-term interest rate models. Another articles of the interest rate model, using Bayesian framework, Jones(2003) published study about nonlinear drift of the interest rate model in detail, and Gray(2005) studied continuous time short rate models and the parameters estimated by Markov chain Monte Carlo(MCMC) method. Sanford and Martin(2006) made estimation using MCMC algorithm and model selection is made by Bayes factors for each model calculated using Savage-Dickey density ratio. In addition, a recent study by Hong and Lin(2006) examined a variety of short-term interest rate mod- els including the single-factor diffusion models, GARCH models, Markov regime-switching models and jump-diffusion models for Chinese rates. However, more useful models which capture the dynamics of the short-term interest rate are needed. In this paper, we suggest two hierarchical Bayes models based on mean reverting model. The parameters of the models are treated as random variables so that we have to consider appropriate prior distributions for them. By regarding parameters as random variables, we can consider that model construction and estimation involve necessarily some uncertainty and utilize the prior information of interest rate. In the first hierarchical Bayes model, we assume that volatility is constant, and in the second one, it depends on the