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Measuring the error of dynamic hedging: a Laplace transform approach

Author

Listed:
  • Flavio Angelini
  • Stefano Herzel

Abstract

We compute the expected value and the variance of the discretization error of delta hedging and of other strategies in the presence of proportional transaction costs. The method, based on Laplace transform, applies to a fairly general class of models, including Black-Scholes, Merton's jump-diffusion and Normal Inverse Gaussian. The results obtained are not asymptotical approximations but exact and efficient formulas, valid for any number of trading dates. They can also be employed under model mispecification, to measure the influence of model risk on a hedging strategy.

Suggested Citation

  • 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.
    • Handle: RePEc:pia:wpaper:33/2007
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    File URL: http://www2.ec.unipg.it/quaderni/quaderno33web_001.pdf
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    Citations

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    Cited by:

    1. St'ephane Goutte & Nadia Oudjane & Francesco Russo, 2013. "Variance optimal hedging for continuous time additive processes and applications," Papers 1302.1965, arXiv.org.
    2. 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.
    3. Damiani, Mirella & Pompei, Fabrizio & Ricci, Andrea, 2011. "Temporary job protection and productivity growth in EU economies," MPRA Paper 29698, University Library of Munich, Germany.
    4. Lin, X. Sheldon & Wu, Panpan & Wang, Xiao, 2016. "Move-based hedging of variable annuities: A semi-analytic approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 40-49.
    5. Silvia Micheli, 2010. "Learning Curve and Wind Power," Quaderni del Dipartimento di Economia, Finanza e Statistica 81/2010, Università di Perugia, Dipartimento Economia.
    6. Flavio ANGELINI & Stefano HERZEL, 2012. "Delta Hedging in Discrete Time under Stochastic Interest Rate," Quaderni del Dipartimento di Economia, Finanza e Statistica 110/2012, Università di Perugia, Dipartimento Economia.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Jan Kallsen & Arnd Pauwels, 2011. "Variance-Optimal Hedging for Time-Changed Levy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(1), pages 1-28.
    14. 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.

    More about this item

    Keywords

    hedging; Laplace transform;

    JEL classification:

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

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