Catastrophe Bond Pricing Research Articles

Pricing Model Construction and Empirical Research on Catastrophe Bond Pricing for Three Major Crops in China

Agricultural disaster risks are significant for the sector's development, and existing risk management tools have limitations.This paper introduces a nationwide catastrophe bond for wheat, maize, and rice , offering broad coverage for China's agriculture. The paper utilizes marginal distribution and Copula function fitting to model the disaster losses of the three major crops from 1990 to 2022. It employs Monte Carlo simulation to generate a 10,000-year event set and rank correlation to align simulated data with real data. The bond price is then calculated using the Wang model, addressing the challenge of data scarcity and providing an innovative approach to catastrophe bond design. The study finds that bond prices increase with the coverage period and risk level, with interest-risk bonds offering higher returns and risks than principal-and-interest risk bonds. Catastrophe bonds present a more stable risk diversification method compared to reinsurance, both in terms of returns and potential losses.To further the development of agricultural catastrophe bonds, the paper recommends optimizing the issuance environment and establishing a robust market infrastructure.

Pricing of insurance-linked securities: a multi-peril approach

In this paper we build a methodology for pricing of insurance-linked securities which are tied to multiple natural catastrophe perils. As a representative example, we construct a multi-peril catastrophe (CAT) bond which can be linked to the industry loss indices or actual losses incurred by an insurer. We provide pricing formulas for such CAT bonds. We illustrate the introduced methodology on the US natural catastrophe data obtained from Property Claim Services (PCS). Within this dataset, we specifically examine two types of risks: losses associated with wind and thunderstorm events, and those linked to winter storm events. Then, we fit and validate the underlying compound non-homogeneous Poisson processes taking into account the fact that the data are left-truncated. The best fitted loss distributions appear to be Burr and Generalised Extreme Value and for the first peril and log-normal for the second. Finally, we visualise the zero-coupon CAT bond prices for the selected best-fitted models.

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

Investor interest in single-regional earthquake catastrophe bonds has the potential to decline in the future. To pique investor interest, disaster bond prices can be determined by decomposed disaster zones using seismic parameters and Space Time Depth Magnitude (STDM) distance. Therefore, this study aims to develop a Decomposition of Disaster Region Using Earthquake Parameters and STDM Distance on the Earthquake Catastrophe Bond Pricing (DECBP) model for a single period. The basic idea of developing the model is to observe earthquake characteristics in an area by clustering the area based on the Earthquake Disaster Risk Index (EDRI), earthquake parameters (earthquake magnitude and depth), and STDM distance. The research and development (R&D) methodology used in this work is pursued through the creation of a mathematical model for calculating the price of earthquake catastrophe bonds over a single period. The development stages carried out are regional decomposition modelling, payment functions modelling, distribution of extreme earthquake magnitude values modelling, prediction of interest rates and coupons, numerical simulations, and analysis of the effect of interest rates, coupons, and the amount of regional decomposition on earthquake bond prices. Interest rates, coupons, and the number of regional decompositions that affect bond prices for earthquake events are the results of the analysis of the model that's been developed. The resulting model in this study is expected to assist the Super Purpose Vehicle (SPV) in determining the price of earthquake bonds and serve as a reference for future researchers developing models for the price of earthquake catastrophe bonds.

Effect of earthquake sequences on risk-based catastrophe bond pricing.

Catastrophe bonds (cat bond in short) are an alternative risk-transfer instrument used to transfer peril-specific financial risk from governments, financial institutions, or (re)insurers, to the capital market. Current approaches for cat bond pricing are calibrated on seismic mainshocks, and thus do not account for potential effects induced by earthquake sequences. This simplifying assumption implies that damage arises from mainshocks only, while aftershocks yield no damage. Postearthquake field surveys reveal that this assumption is inaccurate. For example, in the 2011 Christchurch Earthquake sequence and 2016-2017 Central Italy Earthquake sequence, aftershocks were responsible for higher economic losses when compared to those caused by mainshocks. This article proposes a time-dependent aggregate loss model that takes into account seismicity clustering and damage accumulation effects in the computation of damage. The model is calibrated on the seismic events recorded during the recent 2016-2017 Central Italy Earthquake sequence. Furthermore, the effects of earthquake sequence on cat bond pricing is explored by implementing the proposed model on five Italian municipalities. The investigation showed that neglecting time-dependency may lead to higher difference (up to 45%) in the cat bond price when compared to standardapproaches.

Mitigating wildfire losses via insurance‐linked securities: Modeling and risk management perspectives

AbstractThis paper investigates the use of catastrophe (CAT) bonds as a risk management tool for wildfires. We introduce a set of Bayesian dynamic models designed to accurately represent wildfire losses, allowing a thorough examination of wildfire CAT bond pricing and hedge effectiveness. Our model captures crucial attributes of wildfire data, such as zero inflation, overdispersion, temporal fluctuations, and spatial dependence. Employing extensive quantitative analyses of US wildfire data, we highlight that CAT bonds can substantially mitigate tail risk associated with insurers' liability. Importantly, index‐based CAT bonds, drawing their payouts from aggregate wildfire losses over a larger geographical scope than an insurer's operational area, also provide effective hedges. Our research underscores the potential of wildfire CAT bonds as an enhancement to traditional reinsurance strategies, offering insurers an improved means to manage and mitigate wildfire exposures amidst inherent uncertainties.

A Regional Catastrophe Bond Pricing Model and Its Application in Indonesia’s Provinces

The national scale of catastrophic losses risk linked to state catastrophe bonds (SCB) is enormous. It can reduce investors’ interest in buying them because the capital required and the loss probability are also significant. To overcome this, the SCB can be made on a smaller regional scale, known as a regional catastrophe bond (RCB). Through RCBs, the catastrophic loss risk investors bear becomes smaller, which can increase investors’ interest in buying them. Unfortunately, RCB issuance faced a fundamental obstacle, where its complex pricing model needed further study. Therefore, this study aims to model it. The model uniquely involves the inflation rate modeled using the Fisher equation and the nonbinary scheme of coupon and redemption value payments modeled by a compound Poisson process. In addition, the model is applied to Indonesia’s catastrophe data, resulting in all provinces’ RCB price estimation and the effects of several variables on RCB price. This research can guide the RCB pricing process of the country’s regions. The estimated RCB prices can be used by Indonesia’s government if RCBs are to be issued one day. Finally, the effects of the inflation rate, catastrophe intensity, and geographical location on RCB prices can guide investors in selecting bond portfolios.

A stochastic exposure model for seismic risk assessment and pricing of catastrophe bonds

Risk-based catastrophe bonds require the estimation of losses from the convolution of hazard, exposure and vulnerability models. These models are affected by different uncertainties that arise from the definition of their input parameters. In this paper, we propose a stochastic approach to treat the uncertainty in the asset location and attributes of the exposure model. The proposed method uses the Monte Carlo sampling approach to generate a stochastic exposure database, where each asset location is generated randomly within the geometric bound of the administration, while the asset attributes (i.e. construction type and material, number of storey, building activity type and number of dwelling) are sampled from distributions built from census data. Finally, a sensitivity analysis is performed to investigate the influence of the spatial resolution of the exposure model on the average annual losses (AAL) and catastrophe bond prices. To this end, we implement four exposure models, with spatial resolution at the asset, municipality and province levels, on a study region comprising ten provinces in southern Italy. Compared to the proposed model, the exposure model where assets are relocated and aggregated at the geometric centroid of the municipality underestimates AAL by 8%, while a higher difference (up to 20%) is observed for the exposure model where assets are relocated and aggregated at the geometric centroid of the province. We also consider an exposure model whose asset locations are extracted from publicly available building footprints. Yet, this latter model was incomplete for some provinces resulting in underestimation of AAL up to 90%. Differences in catastrophe bond prices obtained from the four exposure models are less evident, with the exposure model built based on the building footprints showing a difference up to 9.5%.

Estimating flood catastrophe bond prices using approximation method of the loss aggregate distribution: Evidence from Indonesia

Losses experienced by the Indonesian government due to floods are predicted. It is because of the significance of population growth, closure of water catchment areas, and climate change in many regions in Indonesia. The government has tried to reduce the risk but faces insufficient funds. Therefore, new innovative funding sources are essential to overcome these limitations. One way to obtain it is through issuing Flood Catastrophe Bonds (FCB). Unfortunately, Indonesia has had no FCB price estimate until now. On the basis of this problem, this study aims to estimate the FCB price in Indonesia. The primary method used is the approximation method of the aggregate loss distribution. This method can compute the aggregate flood loss cumulative distribution function value faster. The FCB fair price estimation results are cheap because the risk of the instrument is significant. This significant risk is also proportional to the large return. Finally, further analysis shows that in Indonesia, the attachment point of the FCB has a relationship that is in line with the price, while the term of FCB does not. This research is expected to assist the Indonesian government in determining the fair price of FCB in Indonesia. This research can assist the investors in choosing FCB based on expected return, attachment point, and the term they want.

Extremal Analysis of Flooding Risk and Its Catastrophe Bond Pricing

Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang’s transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning.

Catastrophe bond pricing in the primary market: The issuer effect and pricing factors

COVID pandemic has highlighted the importance of hedging against catastrophic events, for which the catastrophe bond market plays a critical role. Our paper develops a two-level modelling and uses a unique, hand-collected dataset, which is one of the largest and most detailed datasets to date containing: 101 different issuers, 794 different bonds, spanning 1997–2020. We identify issuer effects robustly, isolating them from bond specific pricing effects, therefore providing more credible pricing factor results. We find that bond pricing and volatility are heavily impacted by the issuer, causing 26% of total price variation. We also identify specific issuer characteristics that significantly impact bond pricing and volatility, such as the issuer’s line of business accounting for up to 36% of total price variation. We further find that issuer effects are significant over different market cycles and time periods, causing substantial price variation. The size and content of our data also enables us to identify the counter-intuitive relation between bond premiums and maturity, and bond premiums and hybrid bond triggers.

Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach

Earthquake catastrophe bond pricing models (ECBPMs) employ extreme value theory (EVT) to predict severe losses, although studies on EVT’s use in ECBPMs are still rare. Therefore, this study aimed to use a mini-review approach (MRA) to examine the use of EVT and identify the gaps and weaknesses in the methods or models developed. The MRA stages include planning, search and selection, analysis, and interpretation of the results. The selection results showed five articles regarding the application of EVT in ECBPMs. Furthermore, the analysis found the following: First, the generalized extreme value (GEV) could eliminate extreme data in a period. Second, the trigger model using two parameters is better than one, but the study did not discuss the joint distribution of the two parameters. Third, the autoregressive integrated moving average (ARIMA) allows negative values. Fourth, Cox–Ingersoll–Ross (CIR) in-coupon modeling is less effective in depicting the real picture. This is because it has a constant volatility assumption and cannot describe jumps due to monetary policy. Based on these limitations, it is hoped that future studies can develop an ECBPM that reduces the moral hazard.

Pricing hybrid-triggered catastrophe bonds based on copula-EVT model

<abstract><p>This paper presents a hybrid-triggered catastrophe bond (CAT bond) pricing model. We take earthquake CAT bonds as an example for model construction and numerical analysis. According to the characteristics of earthquake disasters, we choose direct economic loss and magnitude as trigger indicators. The marginal distributions of the two trigger indicators are depicted using extreme value theory, and the joint distribution is established by using a copula function. Furthermore, we derive a multi-year hybrid-triggered CAT bond pricing formula under stochastic interest rates. The numerical experiments show that the bond price is negatively correlated with maturity, market interest rate and dependence of trigger indicators, and positively correlated with trigger level and coupon rate. This study can be used as a reference for formulating reasonable CAT bond pricing strategies.</p></abstract>

Hurricane Bond Price Dependency on Underlying Hurricane Parameters

Abstract Hurricane bonds are parametric in nature as they have a dual-exercise structure: the first exercise is conditional on the hurricane’s physical landfall location and the second is conditional upon the embedded option ending in-the-money. We propose a coupled and physically-based hurricane bond pricing model via Monte Carlo simulation that resolves the dual exercise, which was not addressed in extant loss-based catastrophe bond pricing models. This coupled model is developed at the nexus of atmospheric science and finance by integrating hurricane risk modeling and option pricing. By applying this model to price a parametric hurricane bond, we demonstrate how a hurricane bond’s price is sensitive to its underlying hurricane’s physical parameters – genesis, heading, translation speed, velocity, and radius.

Improving CAT bond pricing models via machine learning

Enhanced machine learning methods provide an encouraging alternative to forecast asset prices by extending or generalizing the possible model specifications compared to conventional linear regression methods. Even if enhanced methods of machine learning in the literature often lead to better forecasting quality, this is not clear for small asset classes, because in small asset classes enhanced machine learning methods may potentially over-fit the in-sample data. Against this background, we compare the forecasting performance of linear regression models and enhanced machine learning methods in the market for catastrophe (CAT) bonds. We use linear regression with variable selection, penalization methods, random forests and neural networks to forecast CAT bond premia. Among the considered models, random forests exhibit the highest forecasting performance, followed by linear regression models and neural networks.

Research on the Pricing of Global Drought Catastrophe Bonds

The rapid development of catastrophe bonds provides a new idea for catastrophe risk dispersion, since its traditional means fail to afford the economic losses caused by the global drought catastrophe. With the deepening of the concept of the community with a shared future for mankind, there is an opportunity to issue global drought catastrophe bonds through international cooperation. Based on the data of global drought catastrophe losses from 1900 to 2018, this paper selects 21 countries as the primary participants of international cooperation and studies the pricing of drought catastrophe bonds by the POT model and high quantile estimation. The results show that the first-class bond has a 10% occurrence probability with the trigger point of $252.54 million, and the second-class one has a 35% occurrence probability with the trigger point being $117.13 million. In line with high quartile estimates, the one-year principal-protected catastrophe bonds with a face value of $1,000 are valued at $957.14 and $939.29, respectively. Besides, the principal portion of the lost bonds is $912.50 and $783.04, while the total of it is $867.86 and $626.79, respectively.

CAT BOND PRICING UNDER A PRODUCT PROBABILITY MEASURE WITH POT RISK CHARACTERIZATION

AbstractFrequent large losses from recent catastrophes have caused great concerns among insurers/reinsurers, who then turn to seek mitigations of such catastrophe risks by issuing catastrophe (CAT) bonds and thereby transferring the risks to the bond market. Whereas, the pricing of CAT bonds remains a challenging task, mainly due to the facts that the CAT bond market is incomplete and that the pricing usually requires knowledge about the tail of the risks. In this paper, we propose a general pricing framework based on a product pricing measure, which combines a distorted probability measure that prices the catastrophe risks underlying the CAT bond with a risk-neutral probability measure that prices interest rate risk. We also demonstrate the use of the peaks over threshold (POT) method to uncover the tail risk. Finally, we conduct case studies using Mexico and California earthquake data to demonstrate the applicability of our pricing framework.

Modelling of left-truncated heavy-tailed data with application to catastrophe bond pricing

In this article, we concentrate on modelling heavy-tailed data which can be subjected to left-truncation. We modify an existing procedure for modelling left-truncated data via a compound non-homogeneous Poisson process to make it systematically applicable in the context heavy-tailed data. The introduced procedure can be applied when the underlying severities of the process follow Burr type XII, Generalised Pareto and Generalised Extreme Value distributions by using the Maximum Product of Spacings (MPS) parameter estimation technique. As a natural consequence of the MPS technique, we consider how Moran’s log spacings statistic for testing goodness-of-fit of the severity distributions can be adapted to suit left-truncated data. Thereafter, we compare the performance of this new fitting procedure against traditional maximum likelihood estimation in the context of natural catastrophe loss data, and evidence in favour of MPS is found. Within the context of these data, we also compare our procedure to a one that does not account for left-truncation. We end our contribution by proposing, for our modelling procedure, a Monte Carlo importance sampling algorithm which ensures that large losses are satisfactorily simulated. In closing, we illustrate the potential usage of both the new fitting and simulation procedures by presenting catastrophe bond prices with a trigger based on the analysed heavy-tailed data.

Methodological Considerations in the Statistical Modeling of Catastrophe Bond Prices

AbstractThe problem of specifying and fitting a statistical model of the pricing of property catastrophe risk is addressed from a methodological perspective. Notable 21st century published efforts to do this are reviewed. The problem is framed in a business context and various strategic and tactical issues are investigated. A naïve application of ordinary least squares regression is seen to have undesirable consequences. Alternative approaches are offered, including weighted least squares with weights inversely proportional to capital requirements, and alternative functional forms. Recommendations are offered.

Multiple-Event Catastrophe Bond Pricing Based on CIR-Copula-POT Model

Catastrophe events are attracting increased attention because of their devastating consequences. Aimed at the nonlinear dependency and tail characteristics of different triggered indexes of multiple-event catastrophe bonds, this paper applies Copula function and the extreme value theory to multiple-event catastrophe bond pricing. At the same time, floating coupon and principal payoff structures are adopted instead of fixed coupon and principal payoff structures, to reduce moral hazard and improve bond attractiveness. Furthermore, we develop a CIR-Copula-POT bond pricing model with CIR stochastic rate and estimate flood multiple-event triggered catastrophe bond price using Monte Carlo simulation method. Finally, we implement the sensitivity analysis to show how catastrophe intensity, maturity date, and the dependence affect the prices of catastrophe bonds.

The Drivers of Cat Bond Spread in the Primary Market

The current paper presents an empirical analysis concerning the cat bond spread determinants at the time of issue, to evaluate potential drivers of catastrophe bond prices in the primary market. Starting from the framework description following the main branch of existing literature in this field, the statistical significance of various determinants on the pricing of cat bond is measured, paying attention to a factor representative of economic and financial circumstances and market conditions in general, consequently not associated with the catastrophe risk, namely Libor; it will be considered in order to verify the absence of influence of risk free rate on spread in the primary market. The results achieved provide insight in understanding variation of catastrophe risk prices, by taking into account term structure as well as external conditions, thus evaluating which potential spread determinants could help to improve the explanatory power of an econometric pricing model.