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Efficient hedging: Cost versus shortfall risk


Author Info

  • 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)

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 4 (2000)
    Issue (Month): 2 ()
    Pages: 117-146

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    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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    Related research

    Keywords: Hedging; shortfall risk; efficient hedges; risk management; lower partial moments; convex duality; stochastic volatility;

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    Cited by:
    1. Michael Kohlmann & Shanjian Tang, 2000. "Multi-Dimensional Backward Stochastic Ricatti Equations, and Applications," CoFE Discussion Paper 00-29, Center of Finance and Econometrics, University of Konstanz.
    2. Balder, Sven & Brandl, Michael & Mahayni, Antje, 2009. "Effectiveness of CPPI strategies under discrete-time trading," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 204-220, January.
    3. Minina, Vera & Vellekoop, Michel, 2010. "A risk reserve model for hedging in incomplete markets," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1233-1247, July.
    4. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    5. Leonel Pérez-Hernández, 2005. "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," Department of Economics and Finance Working Papers EC200505, Universidad de Guanajuato, Department of Economics and Finance.
    6. Michael Kohlmann & Shanjian Tang, 2000. "Global Adapted Solution of One-Dimensional Backward Stochastic Riccati Equations, with Application to the Mean-Variance Hedging," CoFE Discussion Paper 00-26, Center of Finance and Econometrics, University of Konstanz.
    7. Peter Lindberg, 2010. "Optimal partial hedging in a discrete-time market as a knapsack problem," Computational Statistics, Springer, vol. 72(3), pages 433-451, December.
    8. Wang, Yumin, 2009. "Quantile hedging for guaranteed minimum death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 449-458, December.
    9. Micha{\l} Barski, 2014. "On the shortfall risk control -- a refinement of the quantile hedging method," Papers 1402.3725,
    10. Mnif, Mohammed & Pham, Huyên, 2001. "Stochastic optimization under constraints," Stochastic Processes and their Applications, Elsevier, vol. 93(1), pages 149-180, May.
    11. Sabrina Mulinacci, 2011. "The efficient hedging problem for American options," Finance and Stochastics, Springer, vol. 15(2), pages 365-397, June.
    12. Paolo Pellizzari, 2003. "Static Hedging of Multivariate Derivatives by Simulation," Finance 0311013, EconWPA, revised 04 Dec 2003.
    13. Bruno Bouchard & Ngoc-Minh Dang, 2013. "Generalized stochastic target problems for pricing and partial hedging under loss constraints—application in optimal book liquidation," Finance and Stochastics, Springer, vol. 17(1), pages 31-72, January.
    14. Melnikov, Alexander & Smirnov, Ivan, 2012. "Dynamic hedging of conditional value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 182-190.
    15. Zhou, Qing & Wu, Weixing & Wang, Zengwu, 2008. "Cooperative hedging with a higher interest rate for borrowing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 609-616, April.
    16. Matos, Joao Amaro de & Lacerda, Ana, 2006. "Equilibrium Bid-Ask Spread of European Derivatives in Dry Markets," FEUNL Working Paper Series wp480, Universidade Nova de Lisboa, Faculdade de Economia.
    17. Heinz Weisshaupt, 2003. "Insuring against the shortfall risk associated with real options," Decisions in Economics and Finance, Springer, vol. 26(2), pages 81-96, November.
    18. Adrien Nguyen Huu & Nadia Oudjane, 2014. "Hedging Expected Losses on Derivatives in Electricity Futures Markets," Papers 1401.8271,
    19. Coleman, Thomas F. & Levchenkov, Dmitriy & Li, Yuying, 2007. "Discrete hedging of American-type options using local risk minimization," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3398-3419, November.
    20. Ilhan, Aytaç & Jonsson, Mattias & Sircar, Ronnie, 2009. "Optimal static-dynamic hedges for exotic options under convex risk measures," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3608-3632, October.
    21. Michael Kohlmann & Shanjian Tang, 2000. "Recent Advances in Backward Stochastics Ricatti Equations and Their Applications," CoFE Discussion Paper 00-30, Center of Finance and Econometrics, University of Konstanz.


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