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Evaluating Discrete Dynamic Strategies in Affine Models

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  • Flavio Angelini
  • Stefano Herzel

Abstract

We consider the problem of measuring the performance of a dynamic strategy, rebalanced at a discrete set of dates, whose objective is that of replicating a claim in an incomplete market driven by a general multi-dimensional affine process. The main purpose of the paper is to propose a method to efficiently compute the expected value and variance of the hedging error of the strategy. Representing the pay-off the claim as an inverse Laplace transform, we are able to get semi-explicit formulas for strategies satisfying a certain property. The result is quite general and can be applied to a very rich class of models and strategies, including Delta hedging. We provide illustrations for the cases of interest rate models and Heston's stochastic volatility model.

Suggested Citation

  • 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.
    • Handle: RePEc:pia:wpaper:71/2009
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    Cited by:

    1. Federico Giorgi & Stefano Herzel & Paolo Pigato, 2024. "A Reinforcement Learning Algorithm For Option Hedging," CEIS Research Paper 586, Tor Vergata University, CEIS, revised 17 Dec 2024.
    2. Damiani, Mirella & Pompei, Fabrizio & Ricci, Andrea, 2011. "Temporary job protection and productivity growth in EU economies," MPRA Paper 29698, University Library of Munich, Germany.
    3. Silvia Micheli, 2010. "Learning Curve and Wind Power," Quaderni del Dipartimento di Economia, Finanza e Statistica 81/2010, Università di Perugia, Dipartimento Economia.
    4. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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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