Abstract
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 this, we generate a stochastic term structure of interest rates as well as stock market returns to simulate investment returns of a stylised life insurance business portfolio in a multi-period setting. On the basis of 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 capitalised 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 payouts to policyholders.
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For a more comprehensive literature review, please refer to a more detailed version of this article available in the ICIR working paper series.
The distinction between book value and market value becomes necessary due to the fact that the profit distribution mechanism is based on German GAAP, that is, book value accounting, whereas Solvency II regulation is based on a market-consistent valuation.
A more comprehensive description of the Japanese case is provided, among others, by Holsboer (2000) and Hoshi and Kashyap (2004).
In the fifth Quantitative Impact Study (QIS 5) (2010), the Risk Margin is defined as “a part of technical provisions” which ensures “that the value of technical provisions is equivalent to the amount that insurance and reinsurance undertakings would be expected to require in order to take over and meet the insurance and reinsurance obligations” in case of insolvency. This is equivalent to the expected cost of capital accruing to the undertaking in the case of portfolio transfer.
Gesamtverband der Deutschen Versicherungswirtschaft e.V.: Statistical Yearbook of German Insurance 2013.
Data is available on the Macro-economic time series database, Money and capital markets, Deutsche Bundesbank.
The CIR model is a wide-spread interest rate model: although its ability to reproduce the observed term structure of interest rates has been challenged over the years (see, for instance, Chan et al., 1992), evidence of its reliability is mixed, with some authors finding major drawbacks (see, for instance, Lamoureux and Witte, 2002) and others finding positive features (see, for instance, Brown and Schaefer, 1994). However, despite its shortcomings, many studies still rely on it (see, for instance, Maurer et al., 2013, and Gerstner et al., 2008). For the purpose of the present paper, the model (and its characteristics) has the desired property of being widely known among researchers and of being relatively easy to calibrate and to adapt to specific needs (i.e. calibration of different interest rate scenarios). Moreover, as pointed out by an anonymous referee, the calibrations that we propose should mitigate some of the undesired properties of the model in the context of a low interest rate environment.
Recent literature has proposed other distributional assumptions that are more robust to market dynamics: for a good overview, see, for instance, Jiménez and Arunachalam (2011).
For a more comprehensive mathematical treatment of the underlying stochastic processes, please refer to a more detailed version of this article available in the ICIR working paper series.
We apply a simplified version of the “minimum value accounting principle”, in German Niederstwertprinzip.
As mentioned in the section “The portfolio structure”, we reproduce an outstanding asset allocation where bonds were bought at different points in time and therefore differ in their time to maturity and coupons. We thus index each bond-like asset class b with a different time to maturity T−τ.
Government Bonds will be discounted using the term structure of interest rates, whereas for the other three asset classes, we will use a discount factor that incorporates the corresponding spread.
This is a necessary assumption, since we do not have any information on the time of the purchase of both stocks and real estate.
We model real estate assets similarly to stocks. Owing to the lack of data, we were not able to estimate the cash flow provided by yearly rents; therefore, we use a simplified approach and treat real estate as stocks.
For a more comprehensive treatment of the regulatory framework, please refer to a more detailed version of this article available in the ICIR working paper series.
In Figure 3, we plot the interest rate on the 10-year maturity German Federal Bond, its 10-year moving average, the 60 per cent of the 10-year moving average and the maximal allowed guaranteed interest rate since 1990; the 60 per cent of the 10-year moving average of the 10-year maturity of the German Federal Bond is used as the basis for the calculation of the maximal allowed guaranteed interest rate. Formally, there is no obligation for life insurers either to provide a minimum guaranteed return or to provide it at the maximum allowed. However, it has become common practice within the industry to provide long-term insurance products that include yearly guaranteed returns set at the maximum allowed by the regulator.
That is, the 10-year moving average of the 10-year German Federal Bond.
Difference between the market value and the book value of tied assets.
The Life Insurance Reform Law (in German Gesetz zur Absicherung stabiler und fairer Leistungen für Lebensversicherte—Lebensversicherungsreformgesetz) was published on 1 August 2014 and entered into force on 6 August 2014.
The reform introduces other substantial modification on the existing regulation but these changes do not affect our model.
The regulatory framework on minimum profit participation entails the possibility for the insurer to reduce the payouts to policyholders if there are unforeseen investment losses or if it is necessary to ensure an insurer's solvency, conditional on the approval of the regulatory authority; this feature has been strengthened by the reform. However such a possibility is close in spirit to a default; therefore we do not take it into consideration in our analysis.
In German Sicherungsbedarf.
We model a product with the main characteristics of an endowment policy in which the premium is normalised to unit.
A thorough discussion on some of these aspects can be found in Babbel (2001). We would like to thank an anonymous referee for pointing out this relevant aspect.
We employ the Fisher–Weil method and use as discount rates the average German yield curve in 2013.
Assekurata market surveys (2012).
Cf. Table 4.
We neglect profits stemming from costs reduction and other sources, since values are persistently negative over time (see Table 5).
The 10-year moving average of the 10-year Government Federal security. See the section “The regulatory framework”.
However, the calculation of the interest rate reserve is based on a 15-year horizon, thus implying that for those contracts with expected residual time to maturity greater than 15 years, the part exceeding 15 years will be discounted using the original discount factor, that is, ri.
Our approach does not lead to a fair valuation as presented among others by Grosen and Løchte Jørgensen (2000) or later by Bauer et al. (2006) and Gatzert (2008). This is due to the fact that our valuation does not include potential additional returns, but only considers the final payment as if the policyholder’s account grew only at the guaranteed return from t onwards. This is justified by the fact that we are mainly interested in assessing the solvency situation of insurers and therefore, since there is no obligation for the insurer to pay additional returns on top of the guaranteed return, we only account for the guaranteed return.
The 2009 Solvency II Directive explicitly recalls the principle of best estimation for the valuation of liabilities. We thus interpret the present value as being the best estimation of the value of the lowest final payment at that particular point in time, recalling the absence of surrender options and mortality risk.
See Article 6,§4 of the Life Insurance Reform Law (in German Lebensversicherungsreformgesetz).
See Article 1,§3 of the Life Insurance Reform Law (in German Lebensversicherungsreformgesetz).
The calculation of
and 
is based on a 15-year horizon.Premiums include those coming from ongoing contracts and from the newly issued cohort of contracts.
We assume that the insurer sells high valuable assets and immediately reinvests an equivalent amount necessary to keep the book value unchanged.
For a more detailed overview of the trading strategy, please refer to a more detailed version of this article available in the ICIR working paper series.
See, for instance, Bauer et al. (2012) and Christiansen and Niemeyer (2012).
Under Solvency II regulations, the CoC is assumed to be fixed at 6 per cent.
For a more comprehensive description of the calibrations, please refer to a more detailed version of this article available in the ICIR working paper series.
Deutscher Aktien IndeX—main German stock index.
Diversified real estate investment trusts (REITS).
As pointed out by an anonymous referee, the mean reversion coefficient (that is, the speed of mean reversion) k is sufficiently low to shelter our simulations from unrealistic behaviour of the short-term interest rate process. In fact, a feature of the quadratic stochastic process used in the model is the non-negativity of the interest rate. This implies that as the process approaches the zero bound level, a relatively high level of mean reversion might cause the interest rate process to quickly jump up to a higher level in a relatively short period of time. As pointed out, among others, by Black (1995), this might be an uncomfortable property in the light of observed interest rate behaviour. In fact, interest rates approaching a very low level seldom recover quickly to their long-run mean, but rather stay at a lower level for a prolonged period of time (Black, 1995).
It is worth noticing that calibration number 3 tries to simulate an interest rate environment similar to the one observed after the introduction of the euro, therefore, still below market returns observed in the 1990s but above the returns observed after the 2008 crisis.
See data in Table 2.
BaFin Statistics on primary insurers, 2012. Data is expressed at book values.
Recalling Eq. (24), the insurer would avoid additional return distribution, since the return on assets is below the return of the policyholders.
Recall constraint 42.
Recall that our trading strategy replaces assets from the most liquid and the closest to maturity to the least liquid and with the longest time to maturity.
The CIR model features a mean reverting process: this implies that given the initial calibration, interest rates tend to be lower at the beginning of the simulation and gradually converge towards the 3 per cent level.
Discount factors for Mortgage Pfandbriefe, Bank Bonds and Corporate Bonds are obtained by adding the liquidity premium on top of the simulated term structure of interest rates.
See, for instance, Rajan (2005) and Antolin et al. (2011).
and 
is based on a 15-year horizon.References
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Berdin, E., Gründl, H. The Effects of a Low Interest Rate Environment on Life Insurers. Geneva Pap Risk Insur Issues Pract 40, 385–415 (2015). https://doi.org/10.1057/gpp.2014.38
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DOI: https://doi.org/10.1057/gpp.2014.38