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Efficient hedging: Cost versus shortfall risk

Author

Listed:
  • Hans FÃllmer

    (Institut fØr Mathematik, Humboldt-UniversitÄt zu Berlin, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

  • Peter Leukert

    (Institut fØr Mathematik, Humboldt-UniversitÄt zu Berlin, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

Abstract

An investor faced with a contingent claim may eliminate risk by (super-) hedging in a financial market. As this is often quite expensive, we study partial hedges which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal probability, given a capital constraint. Here we look for strategies which minimize the shortfall risk defined as the expectation of the shortfall weighted by some loss function. The resulting efficient hedges allow the investor to interpolate in a systematic way between the extremes of no hedge and a perfect (super-) hedge, depending on the accepted level of shortfall risk.

Suggested Citation

  • Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:117-146
    Note: received: November 1998; final version received: March 1999
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    More about this item

    Keywords

    Hedging; shortfall risk; efficient hedges; risk management; lower partial moments; convex duality; stochastic volatility;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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