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Rate Of Convergence Of Monte Carlo Simulations For The Hobson–Rogers Model

Author

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  • FABIO ANTONELLI

    (Dipartimento di Matematica, Università di L'Aquila, Via Vetoio, loc. Coppito L'Aquila, 67100, Italy)

  • VALENTINA PREZIOSO

    (Dipartimento di Matematica, Università di Padova, Via Trieste 63, Padova, 35121, Italy)

Abstract

The Hobson–Rogers model is used to price derivative securities under the no-arbitrage condition in a stochastic volatility setting, preserving the completeness of the market. Here we are studying the rate of convergence of the Euler/Monte Carlo approximations, when pricing European, Asian and digital type options. The aim of the present work is to express the approximation error in terms of the time step size, denoted by h, used for the Euler scheme. We recover an already known result, obtained by other authors using PDE approximations, for European options. Namely we show that for a Lipschitz coefficient of the driving equations for the asset price and Lipschitz payoffs, we obtain an error of the order of $\sqrt{h}$. Moreover, using Malliavin Calculus techniques, we show that with a regular coefficient we may attain an error of the order of h for regular payoffs and of the order of $\sqrt{h}$ for non Lipschitz payoffs. Finally we show some numerical simulations supporting our theoretical results.

Suggested Citation

  • Fabio Antonelli & Valentina Prezioso, 2008. "Rate Of Convergence Of Monte Carlo Simulations For The Hobson–Rogers Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(08), pages 889-904.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:08:n:s021902490800507x
    DOI: 10.1142/S021902490800507X
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    References listed on IDEAS

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    1. Andrea Pascucci & Paolo Foschi, 2005. "Calibration of the Hobson&Rogers model: empirical tests," Finance 0509020, University Library of Munich, Germany.
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    Cited by:

    1. Mauro Rosestolato & Tiziano Vargiolu & Giovanna Villani, 2013. "Robustness for path-dependent volatility models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(2), pages 137-167, November.

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