ifa informiert

Forschung mit Preis ausgezeichnet

Die Arbeit Coherent Projections of Age, Period, and Cohort Dependent Mortality Improvements von Matthias Börger und Marie-Christine Aleksic wurde beim International Congress of Actuaries (ICA) in Washington mit einem „Best Paper Award“ ausgezeichnet.

Der International Congress of Actuaries findet alle vier Jahre statt und ist der weltweit größte Aktuarskongress.

Zusätzlich wurden eine ganze Reihe weiterer Paper von ifa Mitarbeitern für eine Präsentation in Washington ausgewählt:

• Participating Life Insurance Contracts under Risk Based Solvency Frameworks: How to increase Capital Efficiency by Product Design
  Andreas Reuß, Jochen Ruß, Jochen Wieland
• The Impact of Inflation risk on Financial Planning and Risk-Return Profiles
  Stefan Graf, Lena Härtel, Alexander Kling, Jochen Ruß
• It Takes Two: Why Mortality Trend Modeling is more than Modeling One Mortality Trend
  Matthias Börger, Jochen Ruß
• Decomposition of life insurance liabilities into risk factors – theory and application to annuity conversion options
  Daniel Bauer, Marcus C. Christiansen, Alexander Kling, Katja Schilling
• Analysis of objective oriented perspectives for the calculation of Solvency Capital Requirement for pension funds considering Solvency II and IORP II
  Andreas Beckstette, Simona Clever, Hajo Zwiesler

Kurzdarstellung der Forschungsarbeiten:

Participating Life Insurance Contracts under Risk Based Solvency Frameworks: How to increase Capital Efficiency by Product Design
Andreas Reuß, Jochen Ruß, Jochen Wieland

Traditional participating life insurance contracts with year-to-year (cliquet-style) guarantees have come under pressure in the current situation of low interest rates and volatile capital markets, in particular when priced in a market consistent valuation framework. In addition, such guarantees lead to rather high capital requirements under risk based solvency frameworks such as Solvency II or the Swiss Solvency Test (SST). We introduce several alternative product designs and analyze their impact on the insurer’s financial situation. We also introduce a measure for Capital Efficiency that considers both, profits and capital requirements, and compare the results of the innovative products to the traditional product design with respect to Capital Efficiency in a market consistent valuation model.

The Impact of Inflation risk on Financial Planning and Risk-Return Profiles
Stefan Graf, Lena Härtel, Alexander Kling, Jochen Ruß

Thema ist die Leistungsdarstellung von Altersvorsorgeprodukten unter Berücksichtigung des Inflationsrisikos. Um dem Risiko eines eventuellen Kaufkraftverlusts entsprechend Rechnung zu tragen, vergleichen die Autoren reale anstatt nominaler Renditen von Altersvorsorgeprodukten und fokussieren sich dabei insbesondere auf Produkte mit enthaltenen Investmentgarantien. Ihre Analyse zeigt dabei ein signifikantes Inflationsrisiko auf, obwohl nominale Garantien ausgesprochen werden. Daher schlagen die Autoren in Ihrer Arbeit mögliche Absicherungsstrategien vor, untersuchen deren Auswirkungen und kommen dabei zu dem Schluss, dass eine effektive Reduktion des Inflationsrisikos mit dennoch angemessener Kapitalmarktpartizipation dargestellt werden kann.

It Takes Two: Why Mortality Trend Modeling is more than Modeling One Mortality Trend
Matthias Börger, Jochen Ruß

Increasing life expectancy and thus decreasing mortality rates constitute a global trend that can be observed in almost all countries worldwide. Estimating the current rate at which mortality rates decrease and modeling the future rate of decrease is important for e.g. demographers and actuaries. This task is commonly referred to as mortality trend modeling. Recent work, e.g. by (Sweeting, 2011) or (Li, et al., 2011) has established that in many countries the mortality trend appears to be a piecewise linear function. This can be used in stochastic mortality models by implementing trend components that generate a (stochastic) piecewise linear trend and some kind of random fluctuation around this trend. We show that previously discussed versions of this approach have several shortcomings. In particular we show that one needs to distinguish between two different mortality trends: The actual mortality trend (AMT) prevailing at a certain point in time and the estimated mortality trend (EMT) that an observer would estimate given the realized mortality up to that point in time. The difference between these two results from the fact that the AMT is not observable and moreover an observer would not always be able to distinguish between a recent chance in the actual trend and a “normal” random fluctuation around the previous long term trend. Depending on the question at hand, the AMT or the EMT might be the relevant figure to use in analyses. The paper provides a clear definition of and distinction between the actual mortality trend and the estimated mortality trend, discusses their connection, and explains which of the two is relevant for which kind of question. Moreover, a combined model for both trends including a stochastic start trend for the actual mortality trend is specified, and calibrated to mortality data.

Coherent Projections of Age, Period, and Cohort Dependent Mortality Improvements
Matthias Börger, Marie-Christine Aleksic

The projection of future mortality experience constitutes a challenge for both actuaries and demographers. As we show, some of the currently used standard mortality projections have several shortcomings which might pose a serious threat to insurers, pension funds, and social security systems. In this paper, we propose a new projection methodology which overcomes these shortcomings. We introduce a model which allows mortality improvements to depend on age, period, and cohort, and we explain how the model can be estimated and applied. In particular, we show how coherent projections for several populations, i.e. males and females of the same country and populations from closely related countries, can be derived. The basis for these projections are coherent extrapolations of historical life expectancies. As aggregated mortality statistics, life expectancies typically exhibit steady patterns which often makes forecasting rather obvious. We observe that the incorporation of information on the mortality experience of other populations can have a significant impact on the projection for a given population. A comparison with other commonly used projection models shows that our methodology provides stable and highly plausible projections. Finally, we discuss uncertainties in our projection approach and explain how they can be accounted for. In order to illustrate our methodology, we derive fully specified projections for German males and females as members of a large reference set of European populations.

Decomposition of life insurance liabilities into risk factors – theory and application to annuity conversion options
Daniel Bauer, Marcus C. Christiansen, Alexander Kling, Katja Schilling

Life insurance liabilities are influenced by various sources of risk such as equity, interest rate, or mortality risk. Although it is common to measure the total risk via advanced stochastic models, the question of how to allocate the randomness of life insurance liabilities to different sources of risk is not very well understood. In this paper, we first review several proposed decomposition methods and identify serious drawbacks. In diffusion settings, we derive an alternative time-dynamic decomposition method primarily motivated by the martingale representation theorem and show that it overcomes most of the drawbacks identified within other approaches. The proposed decomposition method is applied to several examples from life insurance in order to quantify equity, interest and mortality risks, demonstrating its applicability and usefulness. We show that different life insurance products imply significantly different risk decompositions providing valuable insights for risk management and product design.

Analysis of objective oriented perspectives for the calculation of Solvency Capital Requirement for pension funds considering Solvency II and IORP II
Andreas Beckstette, Simona Clever, Hajo Zwiesler

When entering into long-term commitments one should consider a risk management that ensures the ability to fulfill these obligations. In this context obligations of occupational pensions, which are assumed by employers, life insurers or special institutions for occupational retirement provisions (IORPs), have become a subject of specific interest. The European Commission has already developed a supervisory system for life insurers, called Solvency II. Through the IORP II project initial steps have been taken to revise the current IORP Directive. We will discuss the question of how such a system should be designed for IORPs. At first we will work out the differences between German pension funds and life insurers. The decision, which of these characteristics should be taken into account for the calculation of the Solvency Capital Requirement (SCR), will primarily depend on the objectives set. Possible objectives are the protection of the beneficiary, the employer as the contractual partner of the pension fund, the stability of the system or the avoidance of regulatory arbitrage. Based on these objectives we can derive two possible regulatory perspectives: The first perspective is aimed at the protection of the beneficiary within a system, which is assumed to be stable. The second perspective is targeted toward the following three points: the protection of the contractual partner, the stability of the system and the avoidance of regulatory arbitrage. We will discuss the consequences of these two perspectives with respect to the consideration of the above mentioned specifics for the calculation of the SCR and also further effects and risks. Finally, we will introduce a model which allows the calculation of the SCR for each of the two different perspectives. Using this model, we will analyze the perspectives regarding their impact on the SCR under varying assumptions and different constellations of risk sharing.

Weitere Informationen: