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European Actuarial Journal
Erschienen in: European Actuarial Journal 1/2017

07.02.2017 | Original Research Paper

Market inconsistencies of market-consistent European life insurance economic valuations: pitfalls and practical solutions

verfasst von: Julien Vedani, Nicole El Karoui, Stéphane Loisel, Jean-Luc Prigent

Erschienen in: European Actuarial Journal | Ausgabe 1/2017

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Abstract

The Solvency II directive has introduced a specific so-called risk-neutral framework to valuate economic accounting quantities throughout European life insurance companies. The adaptation of this theoretical notion for regulatory purposes requires the addition of a specific criterion, namely market-consistency, in order to objectify the choice of the valuation probability measure. This paper points out and fixes some of the major risk sources embedded in the current regulatory life insurance valuation scheme. We compare actuarial and financial valuation schemes. We then first address operational issues and potential market manipulation sources in life insurance, induced by both theoretical and regulatory pitfalls. For example, we show that the economic own funds of a representative French life insurance company can vary by almost 140%, as already observed by market practitioners, when the interest rate model is calibrated in October or on the 31st of December. We then propose various modifications of the current implementation, including a first product-specific valuation scheme, to limit the impact of these market-inconsistencies.
Nächster Artikel Runoff or redesign? Alternative guarantees and new business strategies for participating life insurance

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Fußnoten
1
In reality this is an insurance-specific use of the LIBOR Market Model. In particular it is calibrated in a standardized market fashion but the parameters of the calibration date are used for 30–60 years projections. This model is not adapted to such simulations, its first objective being to project the LIBOR forward yield on very short horizons (a few days) for hedging and not to project zero-coupon curves on very long term horizon. For this reason, we denote this model, in its insurance version, by \(LMM_{ins}\) below. The reader may consult the Appendix for further information on this model use and calibration.
 
2
See, e.g., [28, 31].
 
3
See [16] for developments and justification of such treatments, used to formalize, in practice, the idea of “relevant risk-free interest rates term structure”.
 
4
In most other practical fields, when using such types of convergence algorithm, the erratic values after 40 years would be smoothed by the user, in order not to introduce any additional disturbance. It is remarkable that this is not done for the EIOPA yield curve.
 
5
The \(LMM_{ins}\) is only used here for illustration purposes. A pure finance practitioner may find many theoretical and practical issues when using this insurance adaptation of the natural LMM. This question is not developed further here, but will be addressed in subsequent papers.
 
6
We have chosen to consider a \(LMM_{ins}\) because it is currently one of the most-used models, but the results would be similar for other market interest rates models.
 
7
For the 10 randomly drawn curves shown in Fig. 4, we already have two curves capped at 70% and two close to zero.
 
8
These parameters have been chosen because the receiver swaption of maturity 5y/tenor 5y is the most liquid one.
 
9
The choice of 1000 scenarios is a typical number of simulations among European life actuaries. It would of course be desirable to use many more simulations.
 
10
To ease the comparison of the presented results, the numbers have been resized based on a 10,000 basis for 12/31/14 v2.
 
11
Through the Solvency II implementation scheme, products are grouped in ring-fences, and most economic valuations are in fact applied to ring-fenced products. We always speak of valuating products, for the sake of simplicity, but the LMCPM approach developed here, and implemented below, can easily be extended, without loss of generality, to ring-fences of products/liabilities valuations, which may be more useful to practitioners. In particular, a ring-fenced LMCPM measure still leads to a more local and well-adapted market-consistency than a standard valuation approach, where each ring-fenced group of life insurance products is valuated under the same probability measure.
 
12
This is a standard procedure among users of the LIBOR Market Model and its adaptations.
 
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Metadaten
Titel
Market inconsistencies of market-consistent European life insurance economic valuations: pitfalls and practical solutions
verfasst von
Julien Vedani
Nicole El Karoui
Stéphane Loisel
Jean-Luc Prigent
Publikationsdatum
07.02.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
European Actuarial Journal / Ausgabe 1/2017
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-016-0141-z

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