HURRICANE RISK MANAGEMENT WITH CLIMATE AND CO2 INDICES

• Author: Jen‐Wei Yang,Min‐Teh Yu,Chia‐Chien Chang
• DOI: http://doi.org/10.1111/jori.12182
• Date: 01 September 2018
• Published date: 01 September 2018

HURRICANE RISK MANAGEMENT WITH CLIMATE AND

CO

2

INDICES

Chia-Chien Chang

Jen-Wei Yang

Min-Teh Yu

ABSTRACT

We propose a regime-switching Poisson process incorporating climate and

carbon dioxide (CO

2

) indices (RPCM) to model hurricane frequency. Model

accuracy shows that two-state RPCM (2-RPCM) is superior to the existing

climate methods, as forecast errors under 2-RPCM are smaller than previous

models by about 60–75 percent. We derive the pricing formula of reinsurance

premiums by assuming the aggregate loss following the regime-switching

compound process. Pricing errors under 2-RPCM for reinsurance premiums

are 35–54 percent lower than those from previous models. The climate and

regime-switching effects dominate the CO

2

effect in reducing pricing errors

and producing more effective tail value at risk.

INTRODUCTION

Catastrophes (CAT) occur infrequently, but often lead to severe losses. A report from

the Insurance Information Institute indicates that U.S. hurricanes and tropical storms

were responsible for 44 percent of the total losses associated with CAT events from

1991 to 2010. The most costly insured CAT losses in the United States result from

weather-related CAT, in particular, hurricanes (see Table 1). For more accurate

valuations of CAT insurance products and better risk management of hurricane

events, it is thus important to have reliable forecasts of a hurricane frequency

parameter.

Based only on CAT loss data, insurance economists employ a pure Poisson process to

describe the frequency of CAT events to price CAT insurance products (e.g., Chang,

Chang, and Yu, 1996; Lee and Yu, 2002, 2007; Lo, Lee, and Yu, 2013). Lin, Chang, and

Chia-Chien Chang is an Associate Professor in the Department of Finance, National Kaohsiung

University of Applied Science, Taiwan. Chang can be contacted via e-mail: cchiac@kuas.edu.-

tw. Jen-Wei Yang is a Doctoral Candidate in the Department of Finance, National Taiwan

University, Taiwan. Yang can be contacted via e-mail: dor1214@hotmail.com. Min-Teh Yu is at

the Providence University & NCCU—IRRC. Yu can be contacted via e-mail: mtyu@pu.edu.tw.

The authors are thankful for the helpful comments from Dr. Richard MacMinn, Dr. Gene Lai,

Dr. Edward W. Sun, Dr. Edward M. H. Lin, and Dr. Yu-Ren Wang.

© 2016 The Journal of Risk and Insurance. Vol. 85, No. 3, 695–720 (2018).

DOI: 10.1111/jori.12182

695

Powers (2009) point out that the deterministic frequency parameter of the Poisson

process is inadequate for CAT events and propose a doubly stochastic Poisson

process for a frequency parameter of CAT events. Wu and Chung (2010) adopt a

mean-reverting stochastic process as a frequency parameter of CAT events. After

observing the patterns of U.S. hurricane events from 1960 to 2007, Chang, Lin, and Yu

(2011) assume these events follow a two-state Markov-modulated regime-switching

(known as Markov-modulated or regime-switching) Poisson process. However, all

these valuation models of CAT insurance products fail to incorporate important

climate and environmental variables for hurricane risk and are generally incapable of

forecasting future hurricane frequency.

1

Therefore, the main objectives of this article

are to fill this gap in the literature by using regime-switching Poisson regressions to

link the relation between the climate variables and hurricane frequency parameter

and to further examine the impacts of the climate variables on the reinsurance

premiums and tail value at risk (TVaR).

Questions remain about the factors that cause increased hurricane activities. Recent

meteorological studies (e.g., Elsner, Jagger, and Niu, 2000; Maloney and Hartmann,

TABLE 1

Ten Most Costly Catastrophes in the United States

Estimated Insured Losses

Rank Month/Year Event

Amount

When

Occurred

In 2012 Dollars

($billions)

1 Aug. 2005 Hurricane Katrina $41.100 $48.317

2 Sep. 2001 World Trade Center and Pentagon

terrorist attacks

$18.779 $24.345

3 Oct. 2012 Hurricane Sandy $18.750 $18.750

4 Aug. 1992 Hurricane Andrew $15.500 $25.364

5 Jan. 1994 Northridge, CA earthquake $12.500 $19.365

6 Sep. 2008 Hurricane Ike $12.500 $13.329

7 Oct. 2005 Hurricane Wilma $10.300 $12.108

8 Aug. 2004 Hurricane Charley $7.475 $9.085

9 Apr. 2011 Flooding and tornados that struck

Tuscaloosa, AL and other locations

$7.300 $7.451

10 Sep. 2004 Hurricane Ivan $7.110 $8.641

Source: Insurance Services Office, Inc. (ISO), 2013.

1

Curry et al. (2007) note that the approach of integrating relationships derived from historical

data, physical understanding, and climate model projections should be the focus of research

activities in order to project the future risk of hurricane catastrophes in a warmer world. The

recent studies of related CAT risk also focus on the empirical evidence from the primary

market of CAT bonds (Braun, 2015), and the effect of natural CATs or financial crises on CAT

bond premiums (G€

urtler, Hibbeln, and Winkelvos, 2014) or the insurance broker returns

(Ragin and Halek, 2015).

696 THE JOURNAL OF RISK AND INSURANCE