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This paper analyzes the scope of the private market for pandemic insurance. We develop a framework that explains theoretically how the equilibrium price of pandemic insurance depends on accumulation risk, covariance between pandemic claims and other claims, and covariance between pandemic claims and the stock market performance. Using the natural catastrophe (NatCat) insurance market as a laboratory, we estimate the relationship 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 calibrate 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 observed 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%.
Insurance guarantee schemes aim to protect policyholders from the costs of insurer insolvencies. However, guarantee schemes can also reduce insurers’ incentives to conduct appropriate risk management. We investigate stock insurers’ risk-shifting behavior for insurance guarantee schemes under the two different financing alternatives: a flat-rate premium assessment versus a risk-based premium assessment. We identify which guarantee scheme maximizes policyholders’ welfare, measured by their expected utility. We find that the risk-based insurance guarantee scheme can only mitigate the insurer’s risk-shifting behavior if a substantial premium loading is present. Furthermore, the risk-based guarantee scheme is superior for improving policyholders’ welfare compared to the flat-rate scheme when the mitigating effect occurs.
Market risks account for an integral part of life insurers' risk profiles. This paper explores the market risk sensitivities of insurers in two large life insurance markets, namely the U.S. and Europe. Based on panel regression models and daily market data from 2012 to 2018, we analyze the reaction of insurers' stock returns to changes in interest rates and CDS spreads of sovereign counterparties. We find that the influence of interest rate movements on stock returns is more than 50% larger for U.S. than for European life insurers. Falling interest rates reduce stock returns in particular for less solvent firms, insurers with a high share of life insurance reserves and unit-linked insurers. Moreover, life insurers' sensitivity to interest rate changes is seven times larger than their sensitivity towards CDS spreads. Only European insurers significantly suffer from rising CDS spreads, whereas U.S. insurers are immunized against increasing sovereign default probabilities.
This paper sheds light on the life insurance sector’s liquidity risk exposure. Life insurers are important long-term investors on financial markets. Due to their long-term investment horizon they cannot quickly adapt to changes in macroeconomic conditions. Rising interest rates in particular can expose life insurers to run-like situations, since a slow interest rate passthrough incentivizes policyholders to terminate insurance policies and invest the proceeds at relatively high market interest rates. We develop and empirically calibrate a granular model of policyholder behavior and life insurance cash flows to quantify insurers’ liquidity risk exposure stemming from policy terminations. Our model predicts that a sharp interest rate rise by 4.5pp within two years would force life insurers to liquidate 12% of their initial assets. While the associated fire sale costs are small under reasonable assumptions, policy terminations plausibly erase 30% of life insurers’ capital due to mark-to-market accounting. Our analysis reveals a mechanism by which monetary policy tightening increases liquidity risk exposure of non-bank financial intermediaries with long-term assets.
This paper investigates the effects of a rise in interest rate and lapse risk of endowment life insurance policies on the liquidity and solvency of life insurers. We model the book and market value balance sheet of an average German life insurer, subject to both GAAP and Solvency II regulation, featuring an existing back book of policies and an existing asset allocation calibrated by historical data. The balance sheet is then projected forward under stochastic financial markets. Lapse rates are modeled stochastically and depend on the granted guaranteed rate of return and prevailing level of interest rates. Our results suggest that in the case of a sharp increase in interest rates, policyholders sharply increase lapses and the solvency position of the insurer deteriorates in the short-run. This result is particularly driven by the interaction between a reduction in the market value of assets, large guarantees for existing policies, and a very slow adjustment of asset returns to interest rates. A sharp or gradual rise in interest rates is associated with substantial and persistent liquidity needs, that are particularly driven by lapse rates.
Historical evidence like the global financial crisis from 2007-09 highlights that sector concentration risk can play an important role for the solvency of insurers. However, current microprudential frameworks like the US RBC framework and Solvency II consider only name concentration risk explicitly in their solvency capital requirements for asset concentration risk and neglect sector concentration risk. We show by means of US insurers’ asset holdings from 2009 to 2018 that substantial sectoral asset concentrations exist in the financial, public and real estate sector, and find indicative evidence for a sectoral search for yield behavior. Based on a theoretical solvency capital allocation scheme, we demonstrate that the current regulatory approaches can lead to inappropriate and biased levels of solvency capital for asset concentration risk, and should be revised. Our findings have also important implications on the ongoing discussion of asset concentration risk in the context of macroprudential insurance regulation.
Life insurance convexity
(2023)
Life insurers sell savings contracts with surrender options, which allow policyholders to prematurely receive guaranteed surrender values. These surrender options move toward the money when interest rates rise. Hence, higher interest rates raise surrender rates, as we document empirically by exploiting plausibly exogenous variation in monetary policy. Using a calibrated model, we then estimate that surrender options would force insurers to sell up to 2% of their investments during an enduring interest rate rise of 25 bps per year. We show that these fire sales are fueled by surrender value guarantees and insurers’ long-term investments.
Telemonitoring devices can be used to screen consumer characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. Nevertheless, some consumers value their privacy and dislike sharing private information with insurers. In a secondbest efficient Miyazaki-Wilson-Spence (MWS) framework, we allow consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as social welfare. We find that information disclosure can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare. Yet, if all consumers are offered cross-subsidizing contracts, the introduction of a screening contract decreases or even eliminates cross-subsidies. Given the prior existence of a cross-subsidizing MWS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis informs the discussion on consumer protection in the context of digitalization. It shows that new technologies challenge cross-subsidization in insurance markets, and it stresses the negative externalities that digitalization has on consumers who are unwilling to take part in this development.
Low interest rates are becoming a threat to the stability of the life insurance industry, especially in countries such as Germany, where products with relatively high guaranteed returns sold in the past still represent a prominent share of the total portfolio. This contribution aims to assess and quantify the effects of the current low interest rate phase on the balance sheet of a representative German life insurer, given the current asset allocation and the outstanding liabilities. To do so, we generate a stochastic term structure of interest rates as well as stock market returns to simulate investment returns of a stylized life insurance business portfolio in a multi-period setting. Based on empirically calibrated parameters, we can observe the evolution of the life insurers’ balance sheet over time with a special focus on their solvency situation. To account for different scenarios and in order to check the robustness of our findings, we calibrate different capital market settings and different initial situations of capital endowment. Our results suggest that a prolonged period of low interest rates would markedly affect the solvency situation of life insurers, leading to a relatively high cumulative probability of default, especially for less capitalized companies. In addition, the new reform of the German life insurance regulation has a beneficial effect on the cumulative probability of default, as a direct consequence of the reduction of the payouts to policyholders.
This paper is the first to conduct an incentive-compatible experiment using real monetary payoffs to test the hypothesis of probabilistic insurance which states that willingness to pay for insurance decreases sharply in the presence of even small default probabilities as compared to a risk-free insurance contract. In our experiment, 181 participants state their willingness to pay for insurance contracts with different levels of default risk. We find that the willingness to pay sharply decreases with increasing default risk. Our results hence strongly support the hypothesis of probabilistic insurance. Furthermore, we study the impact of customer reaction to default risk on an insurer’s optimal solvency level using our experimentally obtained data on insurance demand. We show that an insurer should choose to be default-free rather than having even a very small default probability. This risk strategy is also optimal when assuming substantial transaction costs for risk management activities undertaken to achieve the maximum solvency level.
This paper compares the shareholder-value-maximizing capital structure and pricing policy of insurance groups against that of stand-alone insurers. Groups can utilise intra-group risk diversification by means of capital and risk transfer instruments. We show that using these instruments enables the group to offer insurance with less default risk and at lower premiums than is optimal for standalone insurers. We also take into account that shareholders of groups could find it more difficult to prevent inefficient overinvestment or cross-subsidisation, which we model by higher dead-weight costs of carrying capital. The tradeoff between risk diversification on the one hand and higher dead-weight costs on the other can result in group building being beneficial for shareholders but detrimental for policyholders.
Socially responsible investing (SRI) continues to gain momentum in the financial market space for various reasons, starting with the looming effect of climate change and the drive toward a net-zero economy. Existing SRI approaches have included environmental, social, and governance (ESG) criteria as a further dimension to portfolio selection, but these approaches focus on classical investors and do not account for specific aspects of insurance companies. In this paper, we consider the stock selection problem of life insurance companies. In addition to stock risk, our model set-up includes other important market risk categories of insurers, namely interest rate risk and credit risk. In line with common standards in insurance solvency regulation, such as Solvency II, we measure risk using the solvency ratio, i.e. the ratio of the insurer’s market-based equity capital to the Value-at-Risk of all modeled risk categories. As a consequence, we employ a modification of Markowitz’s Portfolio Selection Theory by choosing the “solvency ratio” as a downside risk measure to obtain a feasible set of optimal portfolios in a three-dimensional (risk, return, and ESG) capital allocation plane. We find that for a given solvency ratio, stock portfolios with a moderate ESG level can lead to a higher expected return than those with a low ESG level. A highly ambitious ESG level, however, reduces the expected return. Because of the specific nature of a life insurer’s business model, the impact of the ESG level on the expected return of life insurers can substantially differ from the corresponding impact for classical investors.
This paper uses laboratory experiments to provide a systematic analysis of how di↵erent presentation formats a↵ect individuals’ investment decisions. The results indicate that the type of presentation as well as personal characteristics influence both, the consistency of decisions and the riskiness of investment choices. However, while personal characteristics have a larger impact on consistency, the chosen risk level is determined more by framing e↵ects. On the level of personal characteristics, participants’ decisions show that better financial literacy and a better understanding of the presentation format enhance consistency and thus decision quality. Moreover, female participants on average make less consistent decisions and tend to prefer less risky alternatives. On the level of framing dimensions, subjects choose riskier investments when possible outcomes are shown in absolute values rather than rates of return and when the loss potential is less obvious. In particular, reducing the emphasis on downside risk and upside potential simultaneously leads to a substantial increase in risk taking.
The modern tontine: an innovative instrument for longevity risk management in an aging society
(2016)
The changing social, financial and regulatory frameworks, such as an increasingly aging society, the current low interest rate environment, as well as the implementation of Solvency II, lead to the search for new product forms for private pension provision. In order to address the various issues, these product forms should reduce or avoid investment guarantees and risks stemming from longevity, still provide reliable insurance benefits and simultaneously take account of the increasing financial resources required for very high ages. In this context, we examine whether a historical concept of insurance, the tontine, entails enough innovative potential to extend and improve the prevailing privately funded pension solutions in a modern way. The tontine basically generates an age-increasing cash flow, which can help to match the increasing financing needs at old ages. However, the tontine generates volatile cash flows, so that - especially in the context of an aging society - the insurance character of the tontine cannot be guaranteed in every situation. We show that partial tontinization of retirement wealth can serve as a reliable supplement to existing pension products.
Common systemic risk measures focus on the instantaneous occurrence of triggering and systemic events. However, systemic events may also occur with a time-lag to the triggering event. To study this contagion period and the resulting persistence of institutions' systemic risk we develop and employ the Conditional Shortfall Probability (CoSP), which is the likelihood that a systemic market event occurs with a specific time-lag to the triggering event. Based on CoSP we propose two aggregate systemic risk measures, namely the Aggregate Excess CoSP and the CoSP-weighted time-lag, that reflect the systemic risk aggregated over time and average time-lag of an institution's triggering event, respectively. Our empirical results show that 15% of the financial companies in our sample are significantly systemically important with respect to the financial sector, while 27% of the financial companies are significantly systemically important with respect to the American non-financial sector. Still, the aggregate systemic risk of systemically important institutions is larger with respect to the financial market than with respect to non-financial markets. Moreover, the aggregate systemic risk of insurance companies is similar to the systemic risk of banks, while insurers are also exposed to the largest aggregate systemic risk among the financial sector.
Telemonitoring devices can be used to screen consumers' characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. However, some consumers value their privacy and dislike sharing private information with insurers. In the second-best efficient Wilson-Miyazaki-Spence framework, we allow for consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as utilitarian social welfare. Our analysis shows that the choice of information disclosure with respect to revelation of their risk type can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare and a Pareto efficient market allocation. However, if all consumers are offered cross-subsidizing contracts, the introduction of a transparency contract decreases or even eliminates cross-subsidies. Given the prior existence of a WMS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis provides a theoretical foundation for the discussion on consumer protection in the context of digitalization. It shows that new technologies bring new ways to challenge crosssubsidization in insurance markets and stresses the negative externalities that digitalization has on consumers who are not willing to take part in this development.
Life insurance convexity
(2021)
Life insurers massively sell savings contracts with surrender options which allow policyholders to withdraw a guaranteed amount before maturity. These options move toward the money when interest rates rise. Using data on German life insurers, we estimate that a 1 percentage point increase in interest rates raises surrender rates by 17 basis points. We quantify the resulting liquidity risk in a calibrated model of surrender decisions and insurance cash flows. Simulations predict that surrender options can force insurers to sell up to 3% of their assets, depressing asset prices by 90 basis points. The effect is amplified by the duration of insurers' investments, and its impact on the term structure of interest rates depends on life insurers' investment strategy.
Testing frequency and severity risk under various information regimes and implications in insurance
(2023)
We build on Peter et al. (2017) who examined the benefit of testing frequency risk under various information regimes. We first consider testing only severity risk, and whether the principle of indemnity, i.e. the usual contract term that excludes claims payments above the resulting insured loss, affects the insurance contracts offered and purchased. Under information regimes which are less restrictive (in terms of obtaining and using customer information), it is possible for the insurer to offer different contracts for tested and untested individuals. In the absence of the principle of indemnity, individuals will test their severity risk and a separating equilibrium ensues. With the principle of indemnity, given an actuarially fair pooled contract, individuals will not test for severity under less restrictive information regimes; a pooling equilibrium thus ensues. Under more restrictive information regimes, the insurer offers separating contracts. Individuals will test for severity and purchase appropriate contracts. We also consider testing for both frequency and severity risk. The results here are more varied. The highest gain in efficiency from testing results from one of the more restrictive information regimes. Generally under all information regimes, there is a greater gain in efficiency without the principle of indemnity than with the principle of indemnity.
Telemonitoring devices can be used to screen consumer characteristics and mitigate information asymmetries that lead to adverse selection in insurance markets. Nevertheless, some consumers value their privacy and dislike sharing private information with insurers. In a secondbest efficient Miyazaki-Wilson-Spence (MWS) framework, we allow consumers to reveal their risk type for an individual subjective cost and show analytically how this affects insurance market equilibria as well as social welfare. We find that information disclosure can substitute deductibles for consumers whose transparency aversion is sufficiently low. This can lead to a Pareto improvement of social welfare. Yet, if all consumers are offered cross-subsidizing contracts, the introduction of a screening contract decreases or even eliminates cross-subsidies. Given the prior existence of a cross-subsidizing MWS equilibrium, utility is shifted from individuals who do not reveal their private information to those who choose to reveal. Our analysis informs the discussion on consumer protection in the context of digitalization. It shows that new technologies challenge cross-subsidization in insurance markets, and it stresses the negative externalities that digitalization has on consumers who are unwilling to take part in this
development
Market risks account for an integral part of insurers' risk profiles. We explore market risk sensitivities of insurers in the United States and Europe. Based on panel regression models and daily market data from 2012 to 2018, we find that sensitivities are particularly driven by insurers' product portfolio. The influence of interest rate movements on stock returns is 60% larger for US than for European life insurers. For the former, interest rate risk is a dominant market risk with an effect that is five times larger than through corporate credit risk. For European life insurers, the sensitivity to interest rate changes is only 44% larger than toward credit default swap of government bonds, underlining the relevance of sovereign credit risk.