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Hedging error in Lévy models with a Fast Fourier Transform approach

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  • Flavio Angelini
  • Marco Nicolosi

Abstract

We measure, in terms of expectation and variance, the cost of hedging a contingent claim when the hedging portfolio is re-balanced at a discrete set of dates. The basic point of the methodology is to have an integral representation of the payoff of the claim, in other words to be able to write the payoff as an inverse Laplace transform. The models under consideration belong to the class of Lévy models, like NIG, VG and Merton models. The methodology is implemented through the popular FFT algorithm, used by many financial institutions for pricing and calibration purposes. As applications, we analyze the effect of increasing the number of tradings and we make some robustness tests.

Suggested Citation

  • Flavio Angelini & Marco Nicolosi, 2008. "Hedging error in Lévy models with a Fast Fourier Transform approach," Quaderni del Dipartimento di Economia, Finanza e Statistica 43/2008, Università di Perugia, Dipartimento Economia.
  • Handle: RePEc:pia:wpaper:43/2008
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    References listed on IDEAS

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    1. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
    2. Friedrich Hubalek & Jan Kallsen & Leszek Krawczyk, 2006. "Variance-optimal hedging for processes with stationary independent increments," Papers math/0607112, arXiv.org.
    3. Flavio Angelini & Stefano Herzel, 2009. "Evaluating Discrete Dynamic Strategies in Affine Models," Quaderni del Dipartimento di Economia, Finanza e Statistica 71/2009, Università di Perugia, Dipartimento Economia.
    4. 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.
    5. repec:dau:papers:123456789/1392 is not listed on IDEAS
    6. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    7. Helyette Geman & P. Carr & D. Madan & Marc Yor, 2003. "Stochastic Volatility for Levy Processes," Post-Print halshs-00144385, HAL.
    8. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 2001. "Hedging Derivative Securities and Incomplete Markets: An (epsilon)-Arbitrage Approach," Operations Research, INFORMS, vol. 49(3), pages 372-397, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Damiani, Mirella & Pompei, Fabrizio & Ricci, Andrea, 2011. "Temporary job protection and productivity growth in EU economies," MPRA Paper 29698, University Library of Munich, Germany.
    5. 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.
    6. Silvia Micheli, 2010. "Learning Curve and Wind Power," Quaderni del Dipartimento di Economia, Finanza e Statistica 81/2010, Università di Perugia, Dipartimento Economia.
    7. 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.
    8. Marco Nicolosi & Flavio Angelini & Stefano Herzel, 2018. "Portfolio management with benchmark related incentives under mean reverting processes," Annals of Operations Research, Springer, vol. 266(1), pages 373-394, July.

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    More about this item

    Keywords

    Hedging; Lévy models; Fast Fourier Transform;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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