Alexander Kling

A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities

Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk-neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk-neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk-neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance companys risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.

The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees

This paper analyzes the numerical impact of different surplus distribution mechanisms on the risk exposure of a life insurance company selling with profit life insurance policies with a cliquet-style interest rate guarantee. Three representative companies are considered, each using a different type of surplus distribution: A mechanism, where the guaranteed interest rate also applies to surplus that has been credited in the past, a slightly less restrictive type in which a guaranteed rate of interest of 0% applies to past surplus, and a third mechanism that allows for the company to use former surplus in order to compensate for underperformance in “bad” years. Our study demonstrates that regulators should be very careful in deciding which design of a distribution mechanism is to be enforced. Within our model framework, a distribution mechanism of the third type yields preferable results with respect to the considered risk measure. In particular, throughout the analysis, our representative company 3 faces ceteris paribus a significantly lower shortfall risk than the other two companies. Requiring “strong” guarantees puts companies at a significant competitive disad¬vantage relative to insurers which are subject to regulation that only requires the third type of surplus distribution mechanism. This is particularly true, if annual minimum participation in the insurer’s investment returns is mandatory for long term contracts.

Auswirkungen der demografischen Entwicklung auf die Ruhestandsplanung

Die anhaltende Zunahme der Lebenserwartung fuhrt zusammen mit niedrigen Geburtenraten in vielen Landern zu einer starken Veranderung der Bevolkerungsstruktur. Der Anteil der Senioren an der Gesamtbevolkerung wird sich in Zukunft stark erhohen. Dies hat weitreichende Konsequenzen fur alle umlagefinanzierten gesetzlichen Systeme, wie z. B. die gesetzliche Rentenversicherung. Mit vergangenen Rentenreformen wurde im Kern schon beschlossen, dass kunftige Rentnergenerationen ein geringeres Rentenniveau erreichen werden als fruhere Rentnergenerationen. Daher wird ein immer groserer Teil der Bevolkerung den gewunschten Lebensstandard im Alter nur dann halten konnen, wenn zusatzlich zur gesetzlichen Rente noch kapitalgedeckt vorgesorgt wird. Private und betriebliche Altersversorgung werden damit gegenuber gesetzlichen Systemen weiterhin an Bedeutung gewinnen. Aus diesem Grund hat der Staat auch bereits zahlreiche Anreize zur zusatzlichen kapitalgedeckten Vorsorge gesetzt. In diesem Zusammenhang liegt der Fokus der meisten Menschen und Berater bisher aber zu sehr auf dem Sparen fur das Alter. Das Risiko, im Ruhestand langer zu leben, als das angesparte Geld reicht, wird oft ausgeblendet. Die Absicherung dieses Risikos sollte aber ein zentraler Bestandteil der Ruhestandsplanung sein. Rentenversicherungen leisten ein regelmasiges Einkommen – garantiert lebenslang. Sie konnen daher dieses Risiko absichern und im Rahmen der Ruhestandsplanung eine bedeutende Rolle spielen.