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MARKET VALUE MARGIN VIA MEAN–VARIANCE HEDGING

Published online by Cambridge University Press:  18 July 2013

Andreas Tsanakas ,
Mario V. Wüthrich  and
Aleš Černý
Andreas Tsanakas*
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UK
Mario V. Wüthrich
Affiliation:
Department of Mathematics, ETH Zurich, RiskLab, 8092 Zurich, Switzerland
Aleš Černý
Affiliation:
Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, UK
*
E-Mail: [email protected]
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Abstract

We use mean–variance hedging in discrete time in order to value an insurance liability. The prediction of the insurance liability is decomposed into claims development results, that is, yearly deteriorations in its conditional expected values until the liability is finally settled. We assume the existence of a tradeable derivative with binary pay-off written on the claims development result and available in each development period. General valuation formulas are stated and, under additional assumptions, these valuation formulas simplify to resemble familiar regulatory cost-of-capital-based formulas. However, adoption of the mean–variance framework improves upon the regulatory approach by allowing for potential calibration to observed market prices, inclusion of other tradeable assets, and consistent extension to multiple periods. Furthermore, it is shown that the hedging strategy can also lead to increased capital efficiency.

Keywords

Market value marginmean–variance hedgingmarket consistent valuationcost-of-capitalSolvency II
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 43 , Issue 3 , September 2013 , pp. 301 - 322
Copyright
Copyright © ASTIN Bulletin 2013 

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