Securitization of pandemic risk by using coronabond

Abstract

This article investigates the pandemic risk coverage within the European Union member states through insurance securitization. This strategy allows the transfer of health risks from the insurance market to the financial markets. We focus on the financial market crisis caused by the COVID-19 pandemic to securitize the losses caused by the latter. Over the period from 24/01/2020 (the first proven case of contamination in Europe) to 31/03/2020 (end of the dramatic decrease in financial markets), we apply the extreme value theory allowing the selection of the trigger threshold. We identify an immediate reaction of the financial markets following a pandemic shock, the effect of which fades after a few days. The response of stock market indices, measured by the fluctuation of return rates, is not very high. Nevertheless, the reaction of the financial markets is sufficient for the corona bond triggering, provided that the threshold for triggering the incidence rate is optimal. In addition, the securitization of insurance risk could be an alternative process to the classic risk transfer techniques such as co-insurance and reinsurance. Finally, a reinsurance pool dedicated to the insurance scheme's management against the effects of a pandemic is crucial for insurance securitization. These results could have implications for various actors such as insurers, financial investors, and States.

Introduction

The COVID-19 pandemic highlighted the inability of European Union member countries to help each other in the event of a health disaster (Garcia Herrero 2020). Indeed, the most affected countries did not find the necessary support from their European neighbors’, which created palpable tensions at the diplomatic level. The other striking observation is the need to combat this type of scourge on an international scale. One of the main reasons that contributed to the spread of this pandemic is the lack of organization, logistics, and financial means dedicated to such an exceptional situation. The vast majority of countries were caught unawares despite the crisis management and recovery plans put in place after the fact, financed by debt. This observation raises question about the measures to be put in place and the means to be mobilized to face other pandemics that may occur in the future, so as not to make the same mistakes. The means of coverage against catastrophic risks offered by the insurance sector can, for example, enable States to free themselves from their eternal role as the last insurer in times of crisis.

To cover the pandemic risks that could occur in emerging countries, an initial experiment was set up in 2017 by the World Bank with the issue of a pandemic bond. It is considered a financial instrument allowing the transfer of the health risk from the insurance sector to the financial markets and making it possible to have greater financial capacity. Pandemic bonds issued by the World Bank have several shortcomings and restrictive criteria. Indeed, the trigger for the remittance mechanism is based on a rather complex formula that takes into account three conditions: the minimum number of deaths in the country of origin where the epidemic has occurred (from 250 deaths), the minimum number of deaths in another country (from 20 deaths) and the acceleration of the number of the infections. These three conditions make the triggering of the requirement unlikely. The parameter based on the number of deaths has been long and harshly criticized by specialists. In addition, the capacity offered by this instrument with only US$ 195 million is insufficient compared to the financial consequences that could be generated by a pandemic. Moreover, these funds could only be transferred to one of the "poor" countries on the World Bank's list, excluding de facto all other countries. 100 days must elapse after the beginning of the pandemic for the World Bank to respond and determine whether the trigger conditions are realized. Thus, the mechanism can only be triggered when the situation deteriorates further. Finally, to attract investors to subscribe to pandemic bonds, the World Bank has granted interest rates that are considered exorbitant (ranging from 12 to 14%). These rates could make the cost of remunerating this instrument excessive compared to the risks backed by them.

Although the academic literature has extensively discussed the benefits of catastrophe bonds, the issue of pandemic risk coverage in the European Union through insurance securitization remains little studied. Moreover, the COVID-19 pandemic showed the limits of the current system in terms of insurance coverage. A high level of capital would be required to credibly ensure economic losses due to a pandemic (Hartwig et al. 2020). Coronabonds is one the most prominent alternatives in European response to the coronavirus crisis (Caracciolo et al. 2020; Didier et al. 2021). Coronabonds, also known as European Safe Bonds or Eurobonds are already widely used in terms of a unified fiscal stimulus by economists and politicians (Blanchard et al. 2017; Brunnermeier et al. 2017; Bénassy-Quéré et al. 2018). However, one of the arguments against Coronabonds in the management of this pandemic crisis is that this one-off mutual European bond issuance would be an unprecedented step (Horn et al. 2020).

The purpose of this paper is to show how the member countries of the European Union could ensure the risk of the next pandemic by transferring it to the financial markets. Thus, the financial markets would finance the risk, the States concentrating themselves on their resources management to protect their economies. We apply the extreme value theory over the period from 24/01/2020 to 31/03/2020. This approach allows the selection of the trigger threshold as an extreme value, given the Coronabond is riskier than a conventional bond. We do not want to apply this trigger in previous pandemics1 but show that it is possible to transfer the risk of a pandemic (with the example of that of COVID-19) to financial markets. Our results are threefold. First, the rate of return of the stock market index could be a trigger to measure the evolution of the pandemic spread. Second, the securitization of insurance risk could be an alternative process to the classic risk transfer techniques such as co-insurance and reinsurance. Finally, insurance securitization requires a reinsurance pool dedicated to the insurance scheme's management against the effects of a pandemic. The contribution of this article is twofold. First, it contributes to the emerging academic literature on pandemic securitization. Second, it provides insights for a faster and more effective insurance response to manage the spread of a pandemic.

This paper is structured as follows. Section 2 displays the methodology. Section 3 shows the results, discussed in Sect. 4. Section 5 concludes.

Methodology

The first studies of extreme values arose from the need of the astronomers to decide whether to accept or disregard an outlying observation that differs greatly from the rest (Gumbel 1954). Thus, the extreme value theory makes it possible to know the asymptotic behavior of the maxima of values taken by the values of identically distributed and independent random variables (e.g., Embrechts et al. 1999; Coles et al. 2001; De Haan et al. 2006; Resnick 2008). Extreme value theory is applied in many fields such as hydrology, oceanography, epidemiology, demography, insurance, finance, and meteorology. For example, this theory provides a tool for risk managers and allows modeling and anticipation of these risks.

According to Smith (1990), extreme values distribution is as follows. Suppose X₁, X₂, …, are independent random variables with the same probability distribution, and let M_n = max (X₁, …, X_n). Under certain circumstances, normalizing constants exist as follows.

$$\left\{\frac{M_n-b_n}{a_n}\le x\right\}$$

The Three Types Theorem (Fisher and Tippett 1928; Misés 1936; Gnedenko 1943) asserts that if nondegenerate H exists, it must be one of three types:

$$H(x)=exp(-e^{-x}),\text{all}x(\text{Gumbel},1935)$$

$$H(x)=\left\{\begin{array}{c}0\\ \text{exp}\left(-x^{-\alpha }\right)\end{array}\begin{array}{c}x<0\\ x>0\end{array}\right\}(\text{Frechet,}1927)$$

$$H(x)=\left\{\begin{array}{c}\text{exp}\left(-{\left|x\right|}^{\alpha }\right)\\ 1\end{array}\begin{array}{c}x<0\\ x>0\end{array}\right\}(\text{Weibell,}1951)$$

In Fréchet and Weibull,$\alpha >0.$

The three types may be combined into a single generalized extreme value (GEV) distribution.

$$H(x)=exp\left\{-{\left(1+\xi \frac{x-\mu }{\psi }\right)}_{+}^{-1/\xi }\right\}$$

where $\mu$ is a location parameter, $\psi >0$ is a scale parameter, and $\xi$ is a shape parameter. $\xi >0$ corresponds to the Fréchet distribution with $\alpha =1/\xi$.

Results and discussion

Unlike the mechanism proposed by the World Bank where the trigger is based on a rather complex formula, we choose another trigger mechanism. Thus, we investigate whether the rate of returns of the EURO STOXX 50 and FTSEUROFIRST 100 could be a reliable trigger parameter for the Coronabond. There are four main reasons for this choice. First, there is a strong correlation between the rate of return of this index and the COVID-19 pandemic. Second, there is an ability to reduce moral hazard and information asymmetry which are considered key parameters in insurance risk modeling (Gouriéroux 1999; Antonio and Valdez 2012; Crocker and Snow 2013). Third, there is the availability of historical observations over different periods. Finally, there is the possible implementation of a parameter whose threshold is not a function of a certain number of attained deaths. All the calculations are over the period beginning with the first proven case of contamination in Europe (i.e., January 24, 2020) and the end of March 2020 (i.e., March 31, 2020).

Correlation between financial markets and COVID-19

Since the appearance of the first cases of COVID-19 contamination in Europe from 24/01/2020 onwards, the negative impact on the financial markets has not been long in coming. The slowdowns observed in several sectors of activity (e.g., transport, tourism, industry), the total containment imposed by the authorities, and the decline in investor confidence are the main causes of this impact. Figure 1 shows the reaction of the daily values of the stock market indices for each member country, according to the evolution of the number of daily contaminations, during February and March 2020. In the majority of cases, there is a pronounced downward trend from the beginning of February 2020, which continues and stabilizes in the course of March 2020. The economic and health measures implemented by member countries to slow the spread of the pandemic and allow the rescue of the economy may explain this phenomenon. Figure 2 reports the reaction of the EURO STOXX 50 and the FTSEUROFIRST 100. This graph confirms the trend observed on the national indices, i.e., that the overall trend on the European financial markets is downward as soon as the first cases of contamination appear.

Fig. 1.

Trends in the European stock market indices following the outbreak of the COVID-19 pandemic

Fig. 2.

Trends in the EURO STOXX 50 and FTSEUROFIRST 100 following the outbreak of the COVID-19 pandemic

Dependency measurement

We measure the dependency between stock market returns and COVID-19 over the period February–March 2020. We analyze the relationships between the daily rates of return of stock market indices of the European Union member countries and the observations on the daily number of cases reached of COVID-19. Table 1 reports these results. We observe that the average daily rates of return are negative for all the stock market indices with sharp falls sometimes exceeding 10%. This period is also characterized by high volatility with coefficients of variation ranging between 300 and 1500%. March 12, 2020, is the date highlighting the most important bearish peak, i.e., for more than 70% of the markets concerned. In other words, despite the large difference among the cumulative number of infected cases on the day of the downward peak (between 2 and 15,113 cases), the financial markets are impacted identically, indicating the presence of a rapid spread and strong contagion of the stock market shocks. Finally, the correlation coefficient measured between the values of stock market indices and the number of COVID-19 contaminations is negative for all financial markets, confirming the downward trends observed previously.

Table 1.

Indicators between daily rates of return of European stock market indices and the number of daily contaminations

Index	MEAN (%)	MIN (%)	MAX (%)	SD (%)	CV (%)	COR (%)	DPI	DPB
AEX	−0.30	−10.75	8.97	2.73	914.46	−63.67	27/02/2020	12/03/2020
ATHEX	−0.74	−13.39	7.78	4.11	555.40	−71.42	26/02/2020	09/03/2020
ATX	−0.66	−13.65	10.74	3.49	527.02	−70.76	25/02/2020	12/03/2020
BEL20	−0.45	−14.21	7.64	3.07	675.42	−55.99	04/02/2020	12/03/2020
BET	−0.43	−9.58	6.15	2.48	574.29	−64.00	26/02/2020	16/03/2020
BUMIX	−0.34	−8.21	5.55	2.40	703.94	−64.96	04/03/2020	11/03/2020
BUX	−0.52	−10.25	4.03	2.01	389.79	−79.91	08/03/2020	09/03/2020
CAC40	−0.42	−12.28	8.39	3.01	708.59	−63.19	24/01/2020	12/03/2020
CROBEX	−0.51	−10.18	5.78	2.51	490.80	−71.44	25/02/2020	12/03/2020
CYPRUS	−0.62	−9.55	2.18	2.14	342.42	−75.08	09/03/2020	09/03/2020
DAX	−0.42	−11.19	10.26	2.75	657.70	−70.22	28/01/2020	12/03/2020
FTSE100	−0.39	−10.87	9.05	2.75	712.20	−56.70	31/01/2020	12/03/2020
FTSEMIB	−0.46	−16.92	8.93	3.46	750.74	−88.78	31/01/2020	12/03/2020
IBEX35	−0.49	−14.06	7.82	3.14	634.32	−69.99	01/02/2020	12/03/2020
ISEQ	−0.48	−9.94	6.94	2.87	603.01	−71.14	28/02/2020	12/03/2020
MSE	−0.31	−3.59	1.74	1.05	337.42	−80.57	07/03/2020	23/03/2020
OMX20	−0.13	−7.52	3.57	1.95	1,463.09	−69.12	27/02/2020	12/03/2020
OMX25	−0.37	−10.13	6.89	2.62	703.52	−77.49	29/01/2020	12/03/2020
OMX30	−0.28	−10.57	7.09	2.52	898.56	−73.22	31/01/2020	12/03/2020
PSI20	−0.40	−9.76	7.82	2.58	647.69	−57.68	02/03/2020	12/03/2020
PX	−0.49	−7.84	7.65	2.45	502.62	−72.55	01/03/2020	12/03/2020
SAX	−0.14	−3.16	2.51	0.89	629.11	−77.31	06/03/2020	17/03/2020
SBITOP	−0.50	−9.84	3.06	2.21	440.98	−83.55	05/03/2020	12/03/2020
WIG20	−0.48	−13.28	6.54	3.03	630.35	−61.54	04/03/2020	12/03/2020

Note: MEAN significates average rate of return; MIN is the minimum value of the rates of return; MAX is the maximum value of the rates of return; SD is the standard deviation; CV is the coefficient of variation; COR is the coefficient of linear correlation between return rates and the number of observed contaminations; DPI is the start date of COVID-19 contamination; DBP represents the date at which the index rate of return reaches its lowest bearish peak

Identically of the measurement of observed trends, we analyze the measurement of dependency at a more global level. Table 2 presents the results for the FTSEUROFIRST 100 and the EURO STOXX over the period from February to March 2020.

Table 2.

Indicators between daily rates of return of FTSEUROFISRT 100 and EURO STOXX 50 and the total number of daily COVID-19 contaminations

INDEX	MEAN (%)	MIN (%)	MAX (%)	VAR (%)	SD (%)	CV (%)	COR (%)	DPI	DPB
EUROFIRST	−0.42	−12.35	9.66	0.09	2.97	703.05	−73.17	24/01/2020	12/03/2020
EUROSTOXX	−0.41	−12.40	9.24	0.09	2.98	731.92	−72.46	24/01/2020	12/03/2020

Note: MEAN significates average rate of return; MIN is the minimum value of the rates of return; MAX is the maximum value of the rates of return; SD is the standard deviation; CV is the coefficient of variation; COR is the coefficient of linear correlation between return rates and the number of observed contaminations; DPI is the start date of COVID-19 contamination; DBP represents the date at which the index rate of return reaches its lowest bearish peak

Results are very similar to those of the stock market indices by country, confirming a generalized trend for the euro area as a whole. The correlation coefficients measured between these two indices and the number of COVID-19 contaminations are close to the average correlation coefficient calculated based on all stock market indices. This allows us to use one of the two stock market indices as an indicator of the behavior of European financial markets in times of pandemic crisis and as a parameter for triggering the Coronabond.

Speed of propagation

The existence of a period between the triggering of the Coronabond and the release of the funds generated by the securitization transaction implies an analysis of the speed of pandemic spread. Therefore, according to the triggering parameter, the Coronabond will be better parameterized. As highlighted previously, European Union countries were all affected by the pandemic on different dates. Socioeconomic and geographical factors could explain this finding. However, we focus on the evolution of the pandemic as a function of the observed response in the financial markets. Thus, to study the speed of spread, we use the mustache boxes of two indicators: the daily rates of return of stock market indices taken as a whole and the daily evolution of the number of cases infected by COVID-19. Figure 3 displays the results.

Fig. 3.

Mustache boxes for indicators of the daily rates of return of European stock market indices and the daily number of COVID-19 infections. Notes: MEAN significates average rate of return; MIN is the minimum value of the rates of return; MAX is the maximum value of the rates of return; SD is the standard deviation; CV is the coefficient of variation; COR is the coefficient of linear correlation between return rates and the number of observed contaminations; NBJ is the number of days until 03/31/2020; NBP is the number of days before reaching the bearish peak; and NBC is the cumulative number of contamination on the day of the peak

First, the speed of the spread of the pandemic among the countries of the European Union, therefore, remains random and relatively slow. Indeed, the number of days between the first infected case and 31/03/2020, varies from 23 to 68 days, with a mean value of 40 days and a standard deviation of 16 days. For potential future pandemics, it could be interesting to act first in the countries where the pandemic appears first, by choosing reliable indicator(s).

Second, there is a large disparity between the date of the first infected case and the date of the largest drop in the rate of return of the stock index. The range is between 1 and 49 days with a mean value of 22 days and a standard deviation of 16 days. The stock market indices are therefore more affected by the trend of the financial markets than by the speed of the spread of the pandemic.

Finally, on the day where the greatest drop in the stock market index rate of return is observed, there is an important disparity of a cumulative number of contaminations. According to the country, the range varied between 2 and 15,113 with a mean value of 1201 cases and a standard deviation of 3143 cases. This cumulative number reached 27,719 for the European Union. Thus, for the effective intervention of the Coronabond, insurance securitization will have to come second, after that of a reinsurance pool dedicated to the management of a compulsory insurance scheme against the effects of a pandemic.

Our results show that the rate of return of a stock market index could be a trigger for the evolution of the spread of a pandemic. It would then be an alternative to other parameters that directly measure the evolution of the spread such as the number of infected cases or the number of deaths. Indeed, there is a strong correlation between the observed values of stock market indices and the number of people infected with COVID-19. The use of a stock market index thus reduces moral hazard since its value is determined by market mechanisms (De Toldi et al. 1995; Fabozzi and Kothari 2008; Hu 2011). Its use also reduces information asymmetry since the values of stock market indices are displayed transparently, even in times of major crisis (Rees and Wambach 2008).

Determination of the triggering threshold

We use the daily historical rates of return of the EURO STOXX 50 as a trigger parameter for the Coronabond. Figure 4 shows the evolution of the daily rates of return of the EURO STOXX 50 over the period 2013–2020.

Fig. 4.

Daily EURO STOXX 50 rates of return

Given that Coronabond is used to cover financial losses, we mainly analyzed negative rates of return. Two downward peaks are exceeding the threshold of (− 5%) in 2015 and 2016 and one peak exceeding the threshold of (− 10%) in 2020. The latter decrease represents a daily loss in terms of the market capitalization of more than €300 billion.

Coronabond being riskier than a conventional bond, to maintain a certain degree of attraction, the trigger threshold selected must necessarily be an extreme value (Haffar and Teulon 2017). This is the condition for the occurrence of another shock that is not economic, namely the occurrence of a pandemic. Thus, the threshold of (− 5%) is the retained break-even point for satisfying investors and ensuring that reinsurance companies have sufficient financial capacity within a reasonable timeframe.

Estimation of exceedance probabilities

To estimate the probabilities of exceeding the daily threshold of (− 5%), negative EURO STOXX 50 rates of return are considered as a parameter of the loss experience. Absolute values are used. The method of quantile–quantile graphs provides an indication of the probable belonging to one of the possible areas of attraction. Figure 5 reports the results.

Fig. 5.

Comparison between quantiles of a variable following a Normal distribution and quantiles of the EURO STOXX 50 rates of return

The dots on the graph tend to disperse upwards indicating that the data are likely derived from a law of Fréchet (Gilleland and Katz 2016). Figure 6 confirms this finding for the distribution of historical EURO STOXX 50 rates of returns. Table 3 displays the estimated values of Frechet's law parameters.

Fig. 6.

Comparison between EURO STOXX 50 rates of return and Frechet’s law distribution

Table 3.

Estimated Fréchet’s Law parameters for EURO STOXX 50 rates of return

Parameters	Values
Location $\left(\widehat{\mu }\right)$	0.004
Scale $\left(\widehat{\sigma }\right)$	0.004
Shape $\left(\widehat{\epsilon }\right)$	0.525

The tail index ε is relatively high indicating that the weight of extremes in the initial distribution is important. This is one reason why Frechet’s law appears a priori to be quite natural in a financial or insurance context. We then model the risk by performing 100,000 simulations in a 5-year cycle corresponding to the lifetime of the Coronabond. For each cycle, we observe whether the EURO STOXX 50 rates of return exceed the fixed threshold (−5%). The number of simulations is recorded in which the rates of return exceeded the threshold before 1, 2, 3, 4, and 5 years, respectively. The density of maximum rates of return in each cycle is reported in Fig. 7. Table 4 displays probabilities of exceeding the 5% threshold.

Fig. 7.

Density of EURO STOXX 50 rates of return

Table 4.

Probabilities of exceeding the 5% threshold

ti (years)	Number of simulations P[i] where the threshold is crossed before ti	ℙQ(τ ≤ ti)	ℙQ(τ > ti)	ℙQ(τ = ti)
t1 = 1	2,111	0.004	0.995	0.004
t2 = 2	4,241	0.008	0.991	0.004
t3 = 3	6,225	0.012	0.987	0.004
t4 = 4	8,163	0.016	0.983	0.003
t5 = 5	10,080	0.020	0.979	0.003

ℙ^Q(τ ≤ t_i) is the probability that the threshold has been crossed before the end of the ith period; ℙ^Q(τ > t_i) is the probability that the threshold has not been crossed before the end of the ith period; ℙ^Q(τ = t_i) is the probability that the threshold was crossed exactly during the ith period, i.e., between t_i-1 and t_i

For the Coronabond to be triggered, two risks must occur at the same time. The first is the occurrence of an epidemic in the form of a pandemic. The second is the decrease in the rate of return of the stock market index below (− 5%). Thus, the probability calculated in the third column of the table is conditional. It is equal to the ratio between the number of simulations where the threshold is crossed and the total number of simulations performed, multiplied by the probability that the state of a pandemic is announced during one of the 5 years in which the Coronabond runs on the financial market. Given that the issuers of the Coronabond anticipate a possible pandemic during the life of this asset, this probability is therefore equal to 1/5 per year. The level of the risky fraction is an essential parameter in investors' underwriting choices. This choice will also have an impact on the financial capacity available to the issuer. Investors’ risk appetite will be a determining factor in the choice of the level of the risk fraction. These bonds are attractive because they have a high probability of generating an above-average return and a low possibility of substantial loss. They present zero systemic risk. Moreover, since there is no significant correlation between these securities and the profitability of the financial markets, it could be appropriate to add such bonds to a portfolio. In the case of an expected return of a Coronabond higher than the risk-free rate, this security then offers the possibility of improving the performance of a diversified portfolio (for example, see Litzenberger et al. (1996), which discuss catastrophe bonds triggered by natural disasters affecting a restricted geographic area). However, pandemic losses are also likely to be correlated with general economic activity. In other words, investors in a Coronabond are likely to suffer losses on this bond and other financial assets.

Discussion

Our results show that a double-trigger bond would have worked in March 2020. However, there is no indication that we will obtain the same results in the case of a new pandemic. The answer to this question is not easy to establish. Indeed, many elements and circumstances can go wrong. For example, depending on how it is defined, the pandemic trigger might not perfectly match the targeted disease events. Moreover, there is no indication that the stock markets will react in an anticipated manner and how strong it will be. To answer this question, we tested the viability of a double-trigger pandemic bond from April 1, 2020, to March 31, 2021, using a VAR model.

We use daily observations of the number of contaminations in Europe. We cannot economically assert that the used model is a structural phenomenon, given the sample size (365 observations). Moreover, the SVEC and SVAR models do not make it possible to detect cointegrations. Thus, we use a VAR model with a single delay. Figure 8 reports the evolution of the rates of return of three European indices (CAC 40, EURO STOXX 50, and FSTE 100) and the incidence rate of COVID-19. The latter represents the ratio between the number of contaminations in Europe and the total population. Over the period studied, the number of contaminations exceeded one million during a single day. Ignoring the y-axis, it appears that the incidence rate of COVID-19 is the least volatile of the four-time series. However, it is the most unstable over the study period, with a peak reaching 277% and a volatility of 38.82%, as indicated in Table 5. In addition, there is high volatility in the rates of return of the stock market indices at the beginning and end of the time series, when the virus was most virulent.

Fig. 8.

Evolution of index return rates and incidence rate from 04/01/2020 to 03/30/2021

Table 5.

Descriptive statistics of the rates of return of stock market indices and the incidence rate of COVID-19

	CAC40	EURO STOXX50	FTSE100	EUROCIR
Nobs	365.000000	365.000000	365.000000	365.000000
NAs	0.000000	0.000000	0.000000	0.000000
Minimum	−0.170392	−0.165717	−0.139760	−2.931996
Maximum	0.204884	0.214447	0.158689	2.772343
1. Quartile	−0.008216	−0.006458	−0.008090	−0.139695
3. Quartile	0.009280	0.008470	0.008557	0.124865
Mean	0.000883	0.000934	0.000732	0.002908
Median	0.000000	0.000000	0.000000	−0.011703
Sum	0.322180	0.340960	0.267251	1.061376
SE Mean	0.002608	0.002464	0.002035	0.020321
LCL Mean	−0.004245	−0.003911	−0.003269	−0.037054
UCL Mean	0.006010	0.005780	0.004733	0.042869
Variance	0.002482	0.002216	0.001511	0.150725
SD	0.049817	0.047075	0.038871	0.388233
Skewness	0.187123	0.251860	0.213503	0.219763
Kurtosis	3.751317	4.800256	3.991747	17.915516

Figure 9 confirms the trends observed in Fig. 8. First, there is a strong positive correlation between the rates of return of stock market indices. Second, there is a weak negative correlation between stock index rates of return with the COVID-19 incidence rate and a minimum correlation close to 0. This result is crucial and significant. Indeed, an opposite finding would have made the corona bond unattractive for investors: a high negative correlation would increase the probability of triggering the corona bond and reduce the gain for investors.

Fig. 9.

Sample covariance vs minimum estimated covariance

The cointegration test indicates the absence of a long-term relationship. Thus, we opt for a vector autoregressive model of order 1 VAR(1) for two reasons. First, empirical studies suggest a single lag for financial series. Second, the spread speed of the COVID-19 virus is considered very rapid during the study period, so significant daily contamination. Table 6 confirms the results of Fig. 9. Indeed, there are positive correlations between the rates of return of stock market indices and negative correlations between the latter and the COVID-19 incidence rate.

Table 6.

VAR(1) model residual correlation matrix

	CAC40	EURO STOXX50	FTSE100	EUROCIR
CAC40	1.0000	0.98392	0.9759	−0.14544
EURO STOXX50	0.9839	1.00000	0.9723	−0.09132
FTSE100	0.9759	0.97229	1.0000	−0.15052
EUROCIR	−0.1454	−0.09132	−0.1505	1.00000

The restriction matrix presented in Table 7 assumes that variations in the CAC40 do not influence variations in the FTSE100 in the short term, so variations in stock market indices do not impact variations in the COVID-19 incidence rate in the short run.

Table 7.

VAR(1) model restriction matrix

	CAC40.l1	EURO STOXX50.l1	FTSE100.l1	EUROCIR.l1
CAC40	1	1	0	0
EURO STOXX50	1	1	1	0
FTSE100	1	1	1	0
EUROCIR	1	1	1	1

The results of the validation tests of the VAR(1) model (Table 8) indicate that the VAR(1) model is a good modeling choice among the four-time series retained in our study.

Table 8.

VAR(1) model validation tests

	Chi-squared	df	p-value
ARCH (multivariate)	1405	500	< 2.2e − 16
JB-test (multivariate)	9442.1	8	< 2.2e − 16
Skewness only (multivariate)	241.02	4	< 2.2e − 16
Kurtosis only (multivariate)	9201.1	4	< 2.2e − 16
Portmanteau test (asymptotic)	2358	240	< 2.2e − 16
Portmanteau test (adjusted)	2419.6	240	< 2.2e − 16
Breusch-Godfrey LM test	727.11	80	< 2.2e − 16

Figure 10 illustrates the responses measured in the fluctuations of stock market index rates of return to the shock realized on the incidence rate, with an effect lasting an average of 5 days. We note that the first response of the indices after one day is a drop in value, with rates of return reaching − 0.65%. Given that the hurdle rates are around − 0.15% on average over the study period, this indicates that the rates of return of stock market indices can be triggering parameters for corona bonds. Indeed, their returns could reach extreme values during a pandemic. Finally, we note that the responses to the shock run out of steam after approximately one week, which leaves a margin for the triggering of compensation.

Fig. 10.

Responses of stock indices to the impulse of shocks carried out on the incidence rate of COVID-19

Tables 9, 10, and 11 indicate that the CAC40 index is the one that has been the most impacted downward and upward following a shock to the number of COVID-19 contaminations.

Table 9.

Response coefficients of stock market indices to the shock on the COVID19 incidence rate

	CAC40	EURO STOXX50	FTSE100
[1]	0.000000e + 00	0.000000e + 00	0.000000e + 00
[2]	−1.799305e − 03	−1.613653e − 03	−1.331080e − 03
[3]	7.618908e − 04	6.869309e − 04	5.632520e − 04
[4]	−3.097605e − 04	−2.793415e − 04	−2.290334e − 04
[5]	1.257863e − 04	1.134350e − 04	9.300799e − 05
[6]	−5.107630e − 05	−4.606106e − 05	−3.776670e − 05
[7]	2.073977e − 05	1.870331e − 05	1.533535e − 05
[8]	−8.421472e − 06	−7.594559e − 06	−6.226988e − 06
[9]	3.419575e − 06	3.083803e − 06	2.528495e − 06
[10]	−1.388533e − 06	−1.252191e − 06	−1.026706e − 06
[11]	5.638197e − 07	5.084577e − 07	4.168984e − 07

Table 10.

Lower band of response coefficients at the 95% confidence level

	CAC40	EURO STOXX50	FTSE100
[1]	0.000000e + 00	0.000000e + 00	0.000000e + 00
[2]	−6.527953e − 03	−5.688788e − 03	−5.107644e − 03
[3]	−8.380644e − 04	−8.853935e − 04	−7.625903e − 04
[4]	−1.144564e − 03	−1.045304e − 03	−8.758592e − 04
[5]	−1.584830e − 04	−1.802019e − 04	−1.542870e − 04
[6]	−1.583815e − 04	−1.539872e − 04	−1.348541e − 04
[7]	−3.852747e − 05	−3.835868e − 05	−3.278193e − 05
[8]	−3.374780e − 05	−3.187877e − 05	−2.754861e − 05
[9]	−8.474742e − 06	−8.176021e − 06	−7.100879e − 06
[10]	−7.385450e − 06	−6.933217e − 06	−5.772444e − 06
[11]	−1.820143e − 06	−1.747981e − 06	−1.574538e − 06

Table 11.

Upper band of response coefficients at the 95% confidence level

	CAC40	EURO STOXX50	FTSE100
[1]	0.000000e + 00	0.000000e + 00	0.000000e + 00
[2]	1.857512e − 03	1.897380e − 03	1.618510e − 03
[3]	3.012262e − 03	2.725563e − 03	2.344464e − 03
[4]	3.527689e − 04	3.975534e − 04	3.369185e − 04
[5]	4.006672e − 04	3.761034e − 04	3.688911e − 04
[6]	7.776215e − 05	8.324311e − 05	7.113291e − 05
[7]	7.335116e − 05	7.000690e − 05	6.015205e − 05
[8]	1.840821e − 05	1.769207e − 05	1.527810e − 05
[9]	1.554682e − 05	1.453353e − 05	1.279533e − 05
[10]	3.903087e − 06	3.779804e − 06	3.338331e − 06
[11]	3.618577e − 06	3.256630e − 06	2.574959e − 06

The variance decomposition illustrated in Fig. 11 indicates that the COVID-19 incidence rate represents a high proportion of the variance measured in the VAR(1) model, given the exceptional nature of the study period marked by a global pandemic.

Fig. 11.

VAR(1) model variance decomposition

Conclusions

Insurers have been the subject of much criticism following the outbreak of the COVID-19 pandemic with a poor communication strategy and an inability to maintain economic activity. No insurance policy taken out by the companies allowed them compensation for sudden operating losses. We highlight solutions to make up for this shortfall in insurance coverage. For example, a reinsurance pool at the European Union level would allow for rapid intervention to control the spread of a pandemic. Reinsurance and insurance companies would have a certain amount of time to estimate the economic losses incurred following the occurrence of the health catastrophe until the Coronabond is triggered. We have also addressed the shortcomings in the World Bank pandemic bond by changing the category and type of trigger. That makes it possible to eliminate some behavior considered in the insurance sector as contrary to practice, increase the compensation capacity available to the issuing body, and extend the scope of insurance securitization to all European Union member countries.

Indeed, catastrophic risks require special insurance management as they are low frequency and high severity (Louaas and Picard 2021). This makes them difficult to model, in particular, because of an insufficient observation history. Moreover, these are risks that cannot be pooled, since they do not adhere to the law of large numbers. Thus, for these various reasons, the classic risk transfer techniques, i.e., co-insurance and reinsurance, have proved to be non-optimal, hence the use of insurance securitization. The securitization of insurance risk consists of an exchange of principal for periodic coupon payments, in which the payment of coupons and/or repayment of principal is conditional on the occurrence of a predefined trigger event. We apply the extreme value theory allowing the selection of the trigger threshold from the first proven case of contamination in Europe (24/01/2020) to the end of the dramatic decrease of financial markets (31/03/2020). Our results are manifold. First, the rate of return of the stock market index could be a trigger to measure the evolution of the pandemic spread. Second, the securitization of insurance risk could be an alternative process to co-insurance and reinsurance. Finally, a reinsurance pool dedicated to the insurance scheme's management against the effects of a pandemic is crucial for insurance securitization. Thus, the VAR model identifies an immediate reaction of the financial markets following a pandemic shock, the effect of which fades after a few days. The response of stock market indices, measured by the fluctuation of return rates, is not very high. Indeed, the database covers a period when the financial markets were generally stable, a consequence of the global decline caused by the COVID-19 crisis. Nevertheless, the reaction of the financial markets is sufficient for the corona bond triggering, provided that the threshold for triggering the incidence rate is optimal.

The structure presented in this paper, therefore, constitutes a kind of interface for the exchange of risks and capital between the insurance industry and the financial market (Cumming and Derrig 1989; Cumming 1991; Gorvett 1999; Cowley and Cummins 2005; Cox et al. 2010). These results could have implications for various actors such as issuers, financial investors, States, societies, and individuals. Indeed, a reinsurance pool containing insurers and States would make it possible to anticipate the stratospheric costs linked to a pandemic and focus on the essentials, namely the protection of the population and the safeguarding of the economy. Institutional investors could also find a financing and diversification solution with possible gains. This last point could be the subject of future research. In addition, applying a similar methodology based on the incidence rate would confirm or refute our results.

Biographies

Adlane Haffar

has an HDR and Ph.D. in Economics and Applied Statistics and a postgraduate degree in Finance option Insurance. He currently works as a Lecturer at the Faculty of Mathematics of University of Boumediene (Algeria) and Actuarial Expert. His field research revolves mainly around market finance, insurance, and actuarial sciences. He has several publications in journals such as The Quarterly Review of Economics and Finance, the Journal of Asset Management, the Revue d’Economie Financière, and Gestion 2000.

Éric Le Fur

has an HDR and a Doctorate in Economics from the University of Bordeaux. He teaches wealth management, asset management, financial engineering, real estate, and valuation methods. He is a founding member of the Wines and Spirits Chair of INSEEC Bordeaux. His research focuses on the price determinants of alternative assets (fine wines, classic cars, bitcoin) and financial literacy. He published in Annals of Operations Research, Applied Economics, Applied Economics Letters, Economic Modelling, Emerging Markets Review, International Journal of Finance and Economics, Journal of Alternative Investments, Journal of Asset Management, Journal of Wine Economics, Management International, Managerial Finance, Quarterly Review of Economics and Finance, Strategic Change, and Urban Studies.

Mohamed Khordj

has a Doctorate in Economics and Applied Statistics and a postgraduate degree in Finance option Insurance. He works as Casualty, Miscellaneous Risks & NAT-CAT Insurance Manager in Reinsurance Sector. He has several publications in Gestion 2000 and a book entitled “Energy Derivatives and Hedging Strategies” published by Editions Universitaires Européennes.