Abstract
The projection of economic and financial risk factors is a key element of prospective analyzes made by life insurers, both for the calculation of reserves under Solvency 2 and for the asset allocation and management of financial risks. This projection is achieved in practice through “economic scenario generators” (ESG), which are inputs for the calculus of the economic value of assets and liabilities and the analysis of the distribution of this value. The calculation of economic values is based on the “no free lunch” assumption and therefore leads to model the risk factors in a riskneutral probability, while the analysis of the distribution of these values requires the projection of these factors under the historical probability. Therefore, the insurer must handle different representations of the risk factors, which requires looking at the characteristics of a risk neutral ESG, those of an “historical” one and the possible need for coherence between these two representations. This is what we propose to do in this chapter.
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Notes
- 1.
Own Risk and Solvency Assessment. See Guibert et al. [2014] for a thorough analysis of this method.
- 2.
Ifergan (2013) discusses the effectiveness of this scheme from a numerical point of view.
- 3.
The choice is arbitrary in an insurance context, in the sense that the tight relationship in market finance between price calculation and coverage cost is much more tenuous. Choosing a “risk-neutral” probability in an incomplete market is equivalent, in fact, to choosing risks to be covered and those that will not.
- 4.
As with the Vasicek model described in the introduction to this section, which gives a constant price to market risk.
- 5.
Built on the basis of historical Libor rates and used by Caja and Planchet (2010).
- 6.
More generally, changing the measure leaves the dependence structure constant.
- 7.
The rest of this section is based on Planchet and Leroy (2013).
- 8.
Estimation error, here, is understood as the half-width relative to the asymptotic confidence interval at 95 % for the interest size estimator.
- 9.
It may be noted here that the parameters may be different in MCEV and IFRS/Solvency II, even though the underlying model is the same.
- 10.
- 11.
The description of the model as well as the illustration are available at
http://www.ressources-actuarielles.net/C1256F13006585B2/0/A5E99E9ABF5D3674C125772F00600F6C.
- 12.
- 13.
Taken from Planchet and Leroy (2011).
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© 2016 Springer International Publishing Switzerland
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Moudiki, T., Planchet, F. (2016). Economic Scenario Generators. In: Laurent, JP., Norberg, R., Planchet, F. (eds) Modelling in Life Insurance – A Management Perspective. EAA Series. Springer, Cham. https://doi.org/10.1007/978-3-319-29776-7_4
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DOI: https://doi.org/10.1007/978-3-319-29776-7_4
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