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Explicit formulas for the minimal variance hedging strategy in a martingale case

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  • Flavio Angelini
  • Stefano Herzel

Abstract

We explicitly compute the optimal strategy in discrete time for a European option and the variance of the corresponding hedging error under the hypothesis that the underlying is a martingale following a Geometric Brownian motion.
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Suggested Citation

  • Flavio Angelini & Stefano Herzel, 2010. "Explicit formulas for the minimal variance hedging strategy in a martingale case," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 63-79, May.
    • Handle: RePEc:spr:decfin:v:33:y:2010:i:1:p:63-79
    DOI: 10.1007/s10203-009-0097-4
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    References listed on IDEAS

    as
    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. Primbs, James A. & Yamada, Yuji, 2006. "A moment computation algorithm for the error in discrete dynamic hedging," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 519-540, February.
    3. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    4. repec:bla:jfinan:v:44:y:1989:i:5:p:1289-1311 is not listed on IDEAS
    5. Flavio Angelini & Marco Nicolosi, 2010. "On the Effect of Skewness and Kurtosis Misspecification on the Hedging Error," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(3), pages 203-226, November.
    6. Toft, Klaus Bjerre, 1996. "On the Mean-Variance Tradeoff in Option Replication with Transactions Costs," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(2), pages 233-263, June.
    7. Flavio Angelini & Stefano Herzel, 2007. "Measuring the error of dynamic hedging: a Laplace transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 33/2007, Università di Perugia, Dipartimento Economia.
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    Cited by:

    1. Mirella Damiani & Fabrizio Pompei & Andrea Ricci, 2011. "Temporary job protection and productivity growth in EU economies," Quaderni del Dipartimento di Economia, Finanza e Statistica 87/2011, Università di Perugia, Dipartimento Economia.
    2. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2012. "Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets," Papers 1205.4089, arXiv.org.
    3. Ke Nian & Thomas F. Coleman & Yuying Li, 2018. "Learning minimum variance discrete hedging directly from the market," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1115-1128, July.
    4. Davide Castellani & Fabio Pieri, 2011. "Foreign Investments and Productivity Evidence from European Regions," Quaderni del Dipartimento di Economia, Finanza e Statistica 83/2011, Università di Perugia, Dipartimento Economia.
    5. Francesco Venturini, 2011. "Product variety, product quality, and evidence of Schumpeterian endogenous growth: a note," Quaderni del Dipartimento di Economia, Finanza e Statistica 93/2011, Università di Perugia, Dipartimento Economia.
    6. Stefano Herzel & Marco Nicolosi & Cătălin Stărică, 2012. "The cost of sustainability in optimal portfolio decisions," The European Journal of Finance, Taylor & Francis Journals, vol. 18(3-4), pages 333-349, May.
    7. Mirella Damiani, 2010. "Labour regulation, corporate governance and varieties of capitalism," Quaderni del Dipartimento di Economia, Finanza e Statistica 76/2010, Università di Perugia, Dipartimento Economia.
    8. Silvia Micheli, 2010. "Learning Curve and Wind Power," Quaderni del Dipartimento di Economia, Finanza e Statistica 81/2010, Università di Perugia, Dipartimento Economia.

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    More about this item

    Keywords

    Incomplete markets; Hedging; Contingent claim; Variance-optimal hedging;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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