Iterated VaR or CTE Measures: a False Good Idea?

Devolder, Pierre;Lebègue, Adrien
(2014) , 36 pages

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Authors
  • Devolder, PierreUCLouvain
    Author
  • Lebègue, AdrienUCLouvain
    Author
Abstract
The purpose of this paper is twofold. Firstly we consider different risk measures in order to determine the solvency capital requirement of a pension fund. Secondly we illustrate the impact of the time horizon of long-term guarantee products on these capital. We consider a financial market modelled by a common Black-Scholes-Merton model. We neglect the mortality and underwriting risks by assuming that the pension fund is fully hedged against these risks, which allows us to keep understandable and tractable formulæ (the longevity risk will be a part of future researches). A portfolio is built in this market according to different strategies and the pension fund offers a fixed guaranteed rate on a certain time horizon. We begin with well-known static risk measures (value at risk and conditional tail expectation measures) and then we consider their natural dynamic generalization. In order to be time consistent, we consider their iterated versions by a backward iterations scheme. Within the dynamic setting we show that solvency capital can be expensive and that attention must be paid to the safety level considered.
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Devolder, P., & Lebègue, A. (2014). Iterated VaR or CTE Measures: a False Good Idea? (ISBA Discussion Paper 2014/53). https://hdl.handle.net/2078.5/194512