Insurability of pandemic risks

• Published date: 01 December 2021
• Author: Helmut Gründl,Danjela Guxha,Anastasia Kartasheva,Hato Schmeiser
• Date: 01 December 2021
• DOI: http://doi.org/10.1111/jori.12368

Received: 1 December 2020

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Revised: 11 October 2021

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Accepted: 11 October 2021

DOI: 10.1111/jori.12368

ORIGINAL ARTICLE

Insurability of pandemic risks

Helmut Gründl

1

|Danjela Guxha

2

|Anastasia Kartasheva

2,3

|

Hato Schmeiser

2

1

International Center for Insurance

Regulation (ICIR) and Faculty of

Economics and Business, Goethe

University Frankfurt,

Frankfurt, Germany

2

Institute of Insurance Economics,

University of St. Gallen, St. Gallen,

Switzerland

3

Alternative Investments Program,

The Wharton School, University of

Pennsylvania, Philadelphia,

Pennsylvania, USA

Correspondence

Helmut Gründl, International Center for

Insurance Regulation (ICIR) and Faculty

of Economics and Business, Goethe

University Frankfurt,

Theodor‐W.‐Adorno‐Platz 3, D‐60629

Frankfurt am Main, Germany.

Email: gruendl@finance.uni-frankfurt.de

Abstract

This paper analyzes the scope of the private market for

pandemic insurance. We develop a framework that

explains theoretically how the equilibrium price of pan-

demic insurance depends on accumulation risk, covar-

iance between pandemic claims and other claims, and

covariance between pandemic claims and the stock mar-

ket performance. Using the natural catastrophe (NatCat)

insurance market as a laboratory, we estimate the re-

lationship between the insurance price markup and the

tail characteristics of the loss distribution. Then, by using

the high‐frequency data tracking the economic impact of

the COVID‐19 pandemic in the United States, we cali-

brate the loss distribution of a hypothetical insurance

contract designed to alleviate the impact of the pandemic

on small businesses. The pandemic insurance contract

price markup corresponds to the top 20% markup ob-

served in the NatCat insurance market. Then we analyze

an intertemporal risk‐sharing scheme that can reduce the

expected shortfall of the loss distribution by 50%.

KEYWORDS

catastrophe risk transfer, pandemic insurance, private–public

partnerships

JEL CLASSIFICATION

G22, G28, G32, J65, H84, Q54

J Risk Insur. 2021;88:863–902. wileyonlinelibrary.com/journal/JORI

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863

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

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

Association.

1|INTRODUCTION

The economic losses due to the COVID‐19 pandemic are estimated at 3.5% contraction of the

global gross domestic product (GDP) in 2020 (International Monetary Fund, 2021). Business

disruptions have been severe in many sectors of the economy. However, the impact has been

particularly devastating for small‐and medium‐size enterprises in sectors with in‐person in-

teractions, such as tourism, transportation, food, recreation, and others. Furthermore, the

natural science consensus about the increasing frequency of emerging infectious diseases

(Jones et al., 2008; Smith et al., 2014; World Economic Forum, 2019) indicates a growing risk of

global pandemics. How can the insurance industry contribute to building resilience to future

pandemic events? Is pandemic risk insurable? What is the appropriate allocation of functions

between the insurance industry, the financial market, and the government in pandemic risk

transfer?

We develop an initial analysis to address these questions by evaluating the price markup,

that is, the premium in excess of the expected loss, at which a private insurance market is

willing to provide pandemic insurance, theoretically and empirically. We compare the price of

a pandemic insurance contract to the equilibrium prices observed in markets for natural cat-

astrophe (NatCat) risks in the United States. Furthermore, we assess the extent to which the

pandemic insurance price markup can be reduced by an intertemporal risk‐sharing mechanism

to remedy the lack of cross‐sectional diversification in case of a pandemic. Such a mechanism

can be implemented by a long‐term intermediary, such as a government. We also discuss some

of the challenges and limitations of implementing this mechanism.

The analysis is conducted in the context of a hypothetical insurance contract which is

designed to alleviate the economic impact of the pandemic on the revenues and employment of

small‐and medium‐size businesses. The contract provides a monthly compensation during the

pandemic, for either the lost revenues of the business or for the lost employment income of its

workers. Our choice of a hypothetical contract is motivated by the analyses of Chetty et al.

(2020a), as well as Alexander and Karger (2020), that document a sharp reduction in spending

within geographic areas with a high COVID‐19 infection rate and in sectors with in‐person

interaction and mobility during the first quarter of 2020. Consequently, these businesses ex-

perienced a drastic decrease in their revenues and laid off many workers who are primarily

low‐wage workers. This channel accounts for the most sizable economic impact of COVID‐19

in 2020. Between Q1 2020 and Q2 2020, the US GDP fell by $1.73 trillion. The reduction in

consumer spending accounted for $1.35 trillion (an annualized rate of 25%) of the overall GDP

reduction.

Pandemic risk is distinct because of a large accumulation risk, under which many contracts

are triggered within a short period of time (Hartwig et al., 2020; Richter & Wilson, 2020). We

start by providing a theoretical framework that applies the three‐moment capital‐asset pricing

model (CAPM) developed by Kraus and Litzenberger (1976) to characterize the equilibrium of

the pandemic insurance market. Including the third central moment of the claim distribution

into the analysis allows us to map adequately low‐frequency/high‐severity situations and for-

malizes the notion of accumulation risks.

In this setting, we show that the pandemic insurance supply price not only depends on the

covariance between a pandemic risk and the traditional CAPM‐market portfolio, but also on

the covariance between a pandemic risk and all other insured pandemic risks. The resulting

risk charge in the insurance premium reflects the cumulative‐risk character of pandemic risks

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that affect many policyholders simultaneously. In addition, the coskewness of pandemic risks

with capital markets and insurance risks influences the price for pandemic insurance.

Using the same expected‐utility framework that underlies the three‐moments CAPM, we

derive the maximal willingness to pay for a potential policyholder. We elaborate on the con-

ditions under which a market for pandemic risk is possible, that is, we derive the conditions

under which a minimum price of the risk transfer acceptable to an insurer is lower than the

maximum willingness to pay for the risk transfer acceptable to a policyholder.

The theoretical framework formalizes that the equilibrium price of insurance depends on the tail

behavior characteristics of the loss distribution,thecovariancebetweenthepandemicinsurance

losses and losses of other business lines, and the covariance between the pandemic insurance losses

and the stock market returns. We also discuss possible extensions of the model that could lead to an

adjustment of the equilibrium markup, that is, extensions regarding insurers' default risk and

frictional costs, especially through taxes, bankruptcy risk, and agency problems.

Building on the theoretical framework, we develop an empirical assessment of the equili-

brium price markup as a function of the fatness of the tail of the loss distribution and

the covariance of insurers' stock returns with the market portfolio using the catastrophe in-

surance market in the United States as a laboratory. Then we apply the estimated model to

evaluate the price of a hypothetical insurance contract.

For practical reasons the empirical pricing model deviates from the theoretical model. Large

data samples, which are currently not available, would be needed to provide a stable estimation

particularly for the coskewness parameters. Yet, the proposed theoretical pricing model can

serve as a benchmark that shows which parts of the potential markup of a competitive in-

surance premium can already be estimated, and in which direction the empirical markup

calculation can be extended in the future, given improved data availability.

Our empirical assessment of the pandemic insurance price markup is conducted in three

steps. First, we estimate the relationship between the equilibrium insurance price and the tail

characteristics of the loss distribution, relying on extensive data on the NatCat losses, cata-

strophe insurance premiums, and paid losses in the United States. Second, we calibrate the loss

distribution of a hypothetical pandemic insurance contract using the high‐frequency granular

data on business revenues, business closures, employment, and consumer spending in the

United States in 2020. These new and unique data are collected by the Opportunities Insights

Team (OIT) and are presented by Chetty et al. (2020b). We link the economic indicators data to

the weekly infection rates at the county level obtained from the Center for Disease Control

(CDC). By estimating the relationship between the economic indicators and the infection rates,

we calibrate the loss distribution of the pandemic insurance contract and its tail characteristics.

Third, in the last step, we apply the insurance pricing model for natural catastrophes to

evaluate the price markup of a hypothetical pandemic insurance contract and compare it to the

actual equilibrium prices of NatCat insurance in the United States.

Clearly, using a pricing model calibrated to the NatCat market has its shortcomings. In

particular, the NatCat market does not exhibit the significant accumulation risk of the pan-

demic event. However, our study offers an initial estimate of the magnitude of the losses of the

hypothetical pandemic insurance contract and also provides a starting point for further re-

search on the pricing of such a contract.

Next, we summarize the main parts and findings of the empirical analysis. To estimate the

relationship between the markup and the expected shortfall of the loss distribution, we con-

sider a comprehensive sample of the US property–casualty insurers and analyze all business

lines with exposure to natural disasters, including auto physical damage, commercial multiple

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