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Cross-hedging minimum return guarantees: Basis and liquidity risks
Institution:1. Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany;2. Finance Center Muenster, University of Muenster, Universitätsstr. 14-16, D-48143 Münster, Germany;3. Department of Mathematics, Saarland University, PO Box 151150, D-66041 Saarbrücken, Germany;1. Bielefeld University, BiGSEM, Center for Mathematical Economics, PO Box 10 01 31, 33 501 Bielefeld, Germany;2. Paris School of Economics – CNRS, France;3. Université Paris I Panthéon-Sorbonne, Centre d’Economie de la Sorbonne, 106-112 Bd de l’Hôpital, 75647 Paris, France;1. Leica Geosystems Technology A/S, Telehøjen 8, DK-5220 Odense, Denmark;2. Institute of Photogrammetry and GeoInformation, Leibniz Universität Hannover, Nienburger Str. 1, D-30167 Hannover, Germany;3. University of Twente, Hengelosestraat 99, Enschede, The Netherlands;1. Institute for Computational Mechanics and Its Applications (NPUiCMA), Northwestern Polytechnical University, Xi’an, Shaanxi, China;2. Institute of Industrial Science, The University of Tokyo, Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan;3. JST CREST, Gobancho 7, Chiyoda-ku, Tokyo 102-0076, Japan;1. Faculty of Economic Sciences, Chair of Economic Policy and SME Research, University of Goettingen, Platz der Goettinger Sieben 3, 37073 Goettingen, Germany;2. Faculty of Business Administration, Ostfalia University of Applied Sciences Wolfsburg, Siegfried-Ehlers-Str. 1, 38440 Wolfsburg, Germany
Abstract:We reveal pitfalls in the hedging of insurance contracts with a minimum return guarantee on the underlying investment, e.g. an external mutual fund. We analyze basis risk entailed by hedging the guarantee with a dynamic portfolio of proxy assets for the funds. We also take account of liquidity risk which arises since the insurer may need to advance funds for performing the hedge. Based on a least-squares Monte Carlo simulation, we study the economic implications of basis and liquidity risks. We demonstrate that both risks may be surprisingly high and show how the design of the contract and the hedging strategy may help to alleviate them.
Keywords:Basis risk  Least-squares Monte Carlo  Liquidity risk  Periodic premia  Variable annuities
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