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Optimal hedging strategies for multi-period guarantees in the presence of transaction costs: A stochastic programming approach

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  • Fleten, Stein-Erik
  • Lindset, Snorre

Abstract

Multi-period guarantees are often embedded in life insurance contracts. In this paper we consider the problem of hedging these multi-period guarantees in the presence of transaction costs. We derive the hedging strategies for the cheapest hedge portfolio for a multi-period guarantee that with certainty makes the insurance company able to meet the obligations from the insurance policies it has issued. We find that by imposing transaction costs, the insurance company reduces the rebalancing of the hedge portfolio. The cost of establishing the hedge portfolio also increases as the transaction cost increases. For the multi-period guarantee there is a rather large rebalancing of the hedge portfolio as we go from one period to the next. By introducing transaction costs we find the size of this rebalancing to be reduced. Transaction costs may therefore be one possible explanation for why we do not see the insurance companies performing a large rebalancing of their investment portfolio at the end of each year.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 220.

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Date of creation: Oct 2004
Date of revision: Apr 2006
Handle: RePEc:pra:mprapa:220

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Keywords: Multi-period guarantee; Optimal hedging strategies; Transaction costs; Stochastic programming;

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  1. Miltersen, Kristian R. & Persson, Svein-Arne, 1999. "Pricing rate of return guarantees in a Heath-Jarrow-Morton framework," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 307-325, December.
  2. Kozubowski, Tomasz J. & Rachev, Svetlozar T., 1994. "The theory of geometric stable distributions and its use in modeling financial data," European Journal of Operational Research, Elsevier, Elsevier, vol. 74(2), pages 310-324, April.
  3. Boyle, Phelim P & Vorst, Ton, 1992. " Option Replication in Discrete Time with Transaction Costs," Journal of Finance, American Finance Association, American Finance Association, vol. 47(1), pages 271-93, March.
  4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  5. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 7(3), pages 229-263, September.
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