Seasonality in catastrophe bonds and market‐implied catastrophe arrival frequencies

• Published date: 01 September 2021
• Author: Markus Herrmann,Martin Hibbeln
• Date: 01 September 2021
• DOI: http://doi.org/10.1111/jori.12335

Received: 17 October 2019

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Revised: 9 November 2020

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Accepted: 22 November 2020

DOI: 10.1111/jori.12335

ORIGINAL ARTICLE

Seasonality in catastrophe bonds and

market‐implied catastrophe arrival

frequencies

Markus Herrmann |Martin Hibbeln

Mercator School of Management,

University of Duisburg‐Essen,

Duisburg, Germany

Correspondence

Martin Hibbeln, Mercator School

of Management, University of

Duisburg‐Essen, Lotharstr. 65,

47057 Duisburg, Germany.

Email: martin.hibbeln@uni-due.de

Funding information

German Insurance Science Association

(DVfVW)

Abstract

We develop a conceptual framework to model the sea-

sonality in the probability of catastrophe bonds being

triggered. This seasonality causes strong seasonal fluctua-

tions in spreads. For example, the spread on a hurricane

bond is highest at the start of the hurricane season and

declines as time goes by without a hurricane. The spread is

lowest at the end of the hurricane season assuming the

bond was not triggered, and then gradually increases as

the next hurricane season approaches. The model also

implies that the magnitude of the seasonality effect in-

creases with the expected loss and the approaching ma-

turity of the bond. The model is supported by an empirical

analysis that indicates that up to 47% of market fluctua-

tions in the yield spreads on single‐peril hurricane bonds

can be explained by seasonality. In addition, we provide a

method to obtain market‐implied distributions of arrival

frequencies from secondary market spreads.

KEYWORDS

alternative risk transfer, bond spreads, catastrophe arrival

frequencies, seasonality, underwriting risk

JEL CLASSIFICATION

G12; G22

J Risk Insur. 2021;88:785–818. wileyonlinelibrary.com/journal/JORI

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785

This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits

use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or

adaptations are made.

© 2021 The Authors. Journal of Risk and Insurance Published by Wiley Periodicals LLC on behalf of American Risk and Insurance

Association

1|INTRODUCTION

Catastrophe bonds (“cat bonds”) are vehicles to transfer underwriting risk from sponsors,

which are mostly insurance or reinsurance companies but sometimes also corporates or so-

vereigns, to capital markets.

1

The development of the cat bond market mirrors the growing

demand for major natural catastrophe protection. Climate change and growing properties in

coastal areas may have contributed to this demand. Although the main characteristic of cat

bonds is fungibility of catastrophe risk on the secondary market, the knowledge of the

secondary market of cat bonds is sparse. We want to reduce this gap by providing insights into

one of the most important drivers of secondary market spreads: seasonality. Whereas for the

vast majority of traditional corporate bonds there is no clear seasonality of default risk, the

default risk of cat bonds fluctuates with the likelihood of qualifying events, for example, U.S.

hurricanes mostly occur in summer or fall and do not occur in spring. Although seasonality

clearly has an impact on cat bonds, the link between the seasonal nature of catastrophic events

and cat bond spreads is unexplored in the scientific empirical literature.

A typical cat bond pays a flexible coupon that consists of a floating interest rate such as the

LIBOR or a money market rate plus a fixed additional coupon—the risk premium or spread.

While the fixed coupon of a bond remains unchanged, its implicit spread may fluctuate

throughout its lifetime depending on its price on secondary markets. These current secondary

market spreads are of utmost importance to investors and issuers alike: Investors purchase ad-

ditional cat bonds if spreads are high enough to satisfy their risk appetite, whereas they may

refrain from the purchase of new cat bonds on the primary markets if they do not offer the same or

better rates as cat bonds on the secondary markets. Issuers sell additional cat bonds if spreads on

the secondary market for similar risk are lower than rates for traditional reinsurance contracts.

2

The empirical literature on cat bonds rarely investigates secondary market spreads. Braun

(2016) establishes an econometric pricing model to estimate cat bond spreads on primary

markets. Lane and Mahul (2008) investigate the influence of the expected loss, peril type, and

the reinsurance cycle on cat bond spreads. They use secondary market data in form of one

additional observation after issuance for each bond. Dieckmann (2010) uses secondary market

data to investigate the change in reinsurance rates for existing bonds after hurricane Katrina.

However, he abstracts from seasonality in windstorms by assuming constant exogenous

parameters, which can distort empirical results. Braun et al. (2019) indirectly rely on secondary

ILS data by determining common risk factors in ILS fund returns. Gürtler et al. (2016) use

secondary market data to investigate the impact of hurricane Katrina and the default of Leh-

man Brothers on spreads; moreover, they study the impact of bond‐specific factors and mac-

roeconomic variables on cat bond spreads. They acknowledge seasonality effects on secondary

markets but eliminate it by dropping all observations where the time to maturity deviates from

a multiple of a full year, thereby loosing up to 75% of their quarterly observations.

We develop a conceptual framework to model the seasonality in the probability of trigger

events in catastrophe bonds. This conceptual framework has two elements: A hazard rate

1

Cat bonds have importance beyond the insurance sector: For example, developing countries issue cat bonds to receive

payments required for reconstruction and to support the population in case of the occurrence of natural catastrophes.

In 2018 the International Bank for Reconstruction and Development launched a series of cat bonds that protect Latin

American countries from earthquake damages for a total volume of US$ 1360 m. FIFA issued a US$ 262m cat bond to

protect itself against the possible cancelation of the 2006 World Cup in Germany.

2

Braun (2016) provides a detailed description of the structure of a cat bond.

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model and a modeled seasonality measure. (1) Based on the hazard rate model, we illustrate the

theoretical implications for cat bond spreads stemming from seasonal fluctuations in the

probability of a cat bond being triggered. From this hazard rate model, we derive a set of

hypotheses describing the seasonality on the cat bond market, for example, the general pattern

and its increasing amplitude with respect to maturity and riskiness. (2) We derive a compre-

hensible measure to model the seasonal fluctuations in spreads. This measure transforms

seasonally fluctuating arrival frequencies—that is, the distribution of the likelihood of peril

events occurring across 1 year—into the time‐varying expected loss of each individual cat bond.

We support this theoretical framework by analyzing fluctuations of secondary market cat

bond spreads based on a data set that includes 386 seasonality‐affected cat bonds issued be-

tween 2002 and 2017. This data set includes almost the entire cat bond universe. We acquire

these spreads from yearly market reports from Lane Financials LLC. Spreads supplied in these

market reports are quotes surveyed from dealers. These quotes from different dealers are then

averaged across dealers do acquire spreads for individual bonds (Gürtler et al., 2016).

3

In

addition, we show seasonality effects for spreads drawn from actual trading data as reported in

the Trade Reporting and Compliance Engine (TRACE). To the best of our knowledge, we are

the first to use TRACE data on cat bonds in a scientific paper; however, our main analyses rely

on dealer quotes because the available timeframe for the TRACE data started only in 2015 and,

given the low trading frequency for cat bonds, the number of observations is much smaller than

in the quarterly Lane Financials LLC data set. To explain fluctuations on secondary markets,

we use linear fixed effects regression models, thereby explaining the changes in spreads within

each individual bond's observations. We use the relative distributions of arrival frequencies for

hurricanes and European winter storms modeled by Applied Insurance Research (AIR) on a

monthly basis. To obtain these distributions, we were in touch with a representative from AIR

and used information provided in Poliquin and Lalonde (2012). Additionally, we provide a

method to extract market‐implied arrival frequencies from secondary market spreads, thereby

offering an opportunity to access the additional information that investors possess.

We have three main results: First, we document how seasonality affects cat bond spreads.

We find that spreads peak right before the risk season starts and reach their lowest point right

after risk season ends; the amplitude of seasonal fluctuation increases as a bond nears maturity;

in absolute terms, bonds with high expected loss (EL)

4

fluctuate more strongly than bonds with

low EL; single‐peril bonds fluctuate more strongly than multi‐peril bonds. Second, the proposed

“seasonality‐adjusted EL”measure, which is based on the developed conceptual framework,

captures seasonal fluctuations on cat bond spreads. It explains up to 47% of all secondary

market fluctuations among cat bonds that are affected by seasonality (measured by adjusted

within R²). The results on the seasonality measure are strongly supported by the robustness

check with TRACE data. Third, we are able to estimate the market‐implied distributions of

arrival frequencies from secondary market data. These market‐implied distributions explain

secondary market fluctuations as good as modeled distributions of arrival frequencies.

The remainder of this article is as follows: Section 2provides an overview of related lit-

erature. In Section 3, we develop a conceptual framework to model the seasonality in the

probability of catastrophe bonds being triggered and establish hypotheses on seasonality.

Section 4describes the data set. The econometric models are presented in Section 5.

3

Yearly market reports from Lane Financials LLC are available at www.lanefinancialllc.com.

4

The yearly EL can be taken from the cat bond prospectus. Our data source for the EL are yearly market reports from

Lane Financials LLC.

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