A Better Trigger: Indices for Insurance

• Author: Tse‐Ling Teh,Christopher Woolnough
• Date: 01 December 2019
• Published date: 01 December 2019
• DOI: http://doi.org/10.1111/jori.12242

©2018 The Journal of Risk and Insurance. Vol.XX, No. XX, 1–25 (2018).

DOI: 10.1111/jori.12242

A Better Trigger: Indices for Insurance

Tse-Ling Teh

Christopher Woolnough

Abstract

Index triggers have enabled the extension of insurance to a wide range of

risks, by providing a simple mechanism to determine payment. However,

the resulting coverage generates basis risk, the variability over time in the

level of insurance payouts relative to the level of losses. We analyze basis

risk to rank binary and multivalue indices for any risk-averse individual.

Our ranking provides methods to select an index that is optimal for a het-

erogeneous group and illustrates that higher correlation between loss and

index, does not necessarily equate to a better index.

Introduction

In a world of increasing complexity, index triggers offer a simple solution to engage

risk transfer in otherwise untapped markets. Index-based risk transfer is particu-

larly important in developing markets for natural disaster risk because of the limited

availability of other risk transfer options. The growing uncertainty surrounding the

changing state of the natural environment and the increasing financial losses of nat-

ural disasters over the past decades point to considerable risk. At present, this risk

is managed through an ad hoc combination of mitigation, loans, assistance, budget

reallocation, and insurance that can lead to suboptimal outcomes (Lewis and Nicker-

son, 1989; Coate, 1995). This is true at both an individual household and governmental

level.1The potential for index-based insurance to play a larger rolein risk management

has long been identified (Niehaus and Mann, 1992; Goes and Skees, 2003; Linnerooth-

Bayer, Mechler, and Pflug, 2005; Barnett and Mahul, 2007; Ghesquiere and Mahul,

2010), but as yet there is little consolidated theory on how to choose an appropriate

index trigger.This article utilizes expected utility maximization to determine a partial

order ranking of index insurance for any risk-averse individual.

Tse-Ling Teh and Christopher Woolnough are at Maastricht University, Netherlands. Teh can

be contacted via e-mail: t.teh@maastrichtuniversity.nl. Research for this paper was also com-

pleted while Teh was at Columbia University and Woolnough was at New York University.

We would like to thank Geoff Heal, Howard Kunreuther, Daniel Clarke, Daniel Heyen, and

two anonymous referees for their valuable feedback. In addition, the authors are grateful to the

Institute of Actuaries Australia for financial support and the original participants of an index

insurance experiment in Ethiopia that led to the development of this research.

1For example, see Clarke et al. (forthcoming) for details of government disaster

risk-management strategies.

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Under index-based insurance, claims are objectively determined by an index rather

than an individual’s loss level. Examples of such products are weather derivatives

(hot/cold days), catastrophe bonds, and crop insurance (Halcrow, 1949; Froot, 1999).

Indices minimize cross-sectional adverse selection, as individuals pose the same level

of risk to the insurer regardless of their private information. Intertemporal adverse

selection may still exist, as the timing of insurance pricing and the decision to insure

may not coincide; however, an appropriate timing of sales and coverage can help to

minimize this problem.2Moral hazard can be overcome as the risk of a policyholder

depends upon the index, rather than their individual level of risk that is subject to

individual behavior (Miranda, 1991). However, there are limits to the optimality of

index-based risk transfer.

Index-based risk transfer does not provide a perfect hedge and basis risk is generated

with the use of an index as losses are not directly insured.3Basis risk is also present in

other hedging instruments such as futures and options (Figlewski, 1984). Index-based

risk transfer suffers from basis risk in the form of downside basis risk, the chance that

an insurance payout does not match the size of loss, and upside basis risk, the likeli-

hood that a larger insurance payout is received than needed. For example, consider

a rainfall index insurance product used to protect against crop losses. Although the

index aims to protect against crop losses by providing payouts when rainfall is low,

this index does not protect against every crop loss. A form of downside basis risk is if

a crop underperforms despite high rainfall. An individual insuring against crop loss

using an indexed product would not receive a payout if there is adequate rainfall de-

spite suffering crop loss. A form of upside basis risk is an individual who has a good

crop despite inadequate rainfall. This situation can arise from the use of drought-

resistant seed, the storage of water, or an alternative non-rainfall-based water source.

In this case, an individual would receive an insurance payout based on the inadequate

rainfall, despite having a good crop.

A second example of index-based risk transfer is a catastrophe bond. A catastrophe

bond offers protection from natural disasters through an index trigger that can be

parametric or indemnity based.4In the case of a parametric trigger, the trigger is

defined by the physical parameters of the disaster such as the magnitude and lo-

cation. In the case of indemnity-based triggers these tend to be based on modeled

losses or industry loss indices for particular types of disasters. If the index is trig-

gered, then the face value of the catastrophe bond is released to the bond issuer. A

recent example illustrates the importance of the choice of trigger in these bonds. The

Tohoku earthquake that affectedJapan in March 2011 is estimated to have resulted in

2For instance, in the case of weather derivatives therecould be continuous information updating

that may not be possible to include in the insurer’s pricing. To ensure that this information is

not used to intertemporally adversely select against the insurer, an appropriate close of sales

needs to be set. This may be a particular problem for weather derivatives affected by the El

Ni˜

no-Southern Oscillation (ENSO) due to the predictability of outcomes once the episode is

identified.

3In this sense index-based contracts are second best, as they do not cover all the risk. This is

sometimes also termed an incomplete contract (Teh, 2017)

4Or a hybrid between the two indices.

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