The Complementary Compound Truncated Poisson-Weibull Distribution for Pricing Catastrophic Bonds for Extreme Earthquakes

Ismail, Emad A. A.

doi:10.9734/bjemt/2016/26775

Cited by 4 publications

(6 citation statements)

References 7 publications

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“…This final stage resulted in eleven articles that met the criteria. In other words, three articles were deemed not to be appropriate based on the full text: Tao et al [37], Wu and Zou [38], and Ismail [39]. Tao et al [37] discussed the determination of insurance premiums through ECBs, while Wu and Zou [38] and Ismail [39] designed frameworks for calculating the probability of earthquake severity.…”

Section: Article Collection and Selection Resultsmentioning

confidence: 99%

How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework

2023

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Earthquake contingency costs in traditional insurance cannot provide sufficient earthquake funding for a country because they often differ significantly from actual losses. Over the last three decades, this approach has been replaced by linking earthquake insurance to bonds in the capital market; this is now known as the earthquake catastrophe bond (ECB). Through the ECB, contingency costs become larger and more sustainable earthquake funds. Unfortunately, there are challenges in ECB issuance, as the pricing framework does not yet have standard rules and still needs to be studied. Therefore, the objective of this study is to systematically review how the ECB pricing framework is designed. The method used in this review is PRISMA. First, articles aiming to design an ECB pricing framework were collected from the Scopus, Science Direct, and Dimensions databases on 22 March 2023. Then, the results were selected, resulting in eleven relevant articles. Then, the articles’ pricing frameworks were reviewed based on variables, methods, trigger events, coupon and redemption value payment schemes, and the model solution forms. Finally, several research opportunities for academics are also outlined. This research constitutes a reference for ECB issuers during the pricing process and can motivate academics to design more useful ECB pricing models.

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Section: Article Collection and Selection Resultsmentioning

confidence: 99%

How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework

2023

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“…Empirically, the distribution of damage amount from disasters, as a rule, is governed by laws of the heavy tail of the distribution (Rodkin and Pisarenko, 2008). Ismail (2016) has been used the complementary risk method to determine a mixed probability distribution to express the number of accidents and the maximum realized losses (Ismail, 2016 [Louzada et al, 2012].…”

Section: Methodsmentioning

confidence: 99%

“…The results of the test are presented in the Appendix (Ismail, 2016). It can be observed that the value of the test statistic is 0.161, Critical Value is 1.311619 and P-Value is 0.064; which results in non-rejection of the null hypothesis at 5% level.…”

Section: Goodness Of Fitmentioning

confidence: 99%

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Estimating the maximum probable annual losses due to flooding

Ismail¹,

Awwad²

2019

Afr. J. Bus. Manage.

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This paper aims to estimate the maximum probable annual losses to the risks of flooding. While examining the frequency of the event, it was observed that, at least one accident occurred periodically, which resulted in maximum losses. This is an empirical study and it is based on maximum losses due to floods per year, as obtained from the International Disaster Database and Munich Re. The analysis is based on 66 extreme flood events in the world between 1906 and 2015. The complementary risk method has been used in deriving a mixed probability distribution, which expresses the number of floods and the maximum losses realized, where zero-truncated Poisson distribution is used for frequency distribution and Last order Weibull distribution for losses. The maximum of flood losses was fitted with compound truncated Poisson-Weibull distribution. Probabilities have been calculated for extreme flood losses, which are less than specific descriptive measures, and expected values have been calculated for extreme flood losses, which exceed the specific descriptive measures. The results from the study indicate that the maximum probable losses are greater than the maximum actual losses. This paper contributes to the risk of extreme floods pricing; and it also helps the governments of the countries in calculating the financial reserves to cover the extreme flood losses.

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“…An analysis of data from the International Disaster Database (accessed on 28 October 2022 from https://www.emdat.be) shows that, on average, a single extreme earthquake results in economic damage of USD 1,266,348,909, with the highest magnitude compared to other extreme disasters, as illustrated in Figure 1. This high loss burdens the budgets of earthquakeprone countries (countries whose territories lie atop tectonic plate lines) [4][5][6][7], so several of them used traditional insurance mechanisms to obtain contingency funds for mitigation from 1992 to 2000. However, this mechanism generally has shortcomings, whereby the provided contingency costs pale in comparison to the actual losses incurred [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength

Ibrahim,

Sukono,

Napitupulu

et al. 2024

Mathematics

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Traditional insurance’s earthquake contingency costs are insufficient for earthquake funding due to extreme differences from actual losses. The earthquake bond (EB) links insurance to capital market bonds, enabling higher and more sustainable earthquake funding, but challenges persist in pricing EBs. This paper presents zero-coupon and coupon-paying EB pricing models involving the inconstant event intensity and maximum strength of extreme earthquakes under the risk-neutral pricing measure. Focusing on extreme earthquakes simplifies the modeling and data processing time compared to considering infinite earthquake frequency occurring over a continuous time interval. The intensity is accommodated using the inhomogeneous Poisson process, while the maximum strength is modeled using extreme value theory (EVT). Furthermore, we conducted model experiments and variable sensitivity analyses on EB prices using earthquake data from Indonesia’s National Disaster Management Authority from 2008 to 2021. The sensitivity analysis results show that choosing inconstant intensity rather than a constant one implies significant EB price differences, and the maximum strength distribution based on EVT matches the data distribution. The presented model and its experiments can guide EB issuers in setting EB prices. Then, the variable sensitivities to EB prices can be used by investors to choose EB according to their risk tolerance.

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The Complementary Compound Truncated Poisson-Weibull Distribution for Pricing Catastrophic Bonds for Extreme Earthquakes

Cited by 4 publications

References 7 publications

How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework

How to Price Catastrophe Bonds for Sustainable Earthquake Funding? A Systematic Review of the Pricing Framework

Estimating the maximum probable annual losses due to flooding

Earthquake Bond Pricing Model Involving the Inconstant Event Intensity and Maximum Strength

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