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Speed of convergence of the threshold estimator of integrated variance

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  • Cecilia Mancini

    () (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

Abstract

In this paper we consider a semimartingale model for the evolution of the price of a financial asset, driven by a Brownian motion (plus drift) and possibly infinite activity jumps. Given discrete observations, the threshold estimator is able to separate the integrated variance from the sum of the squared jumps. This has importance in measuring and forecasting the asset risks. The exact convergence speed was found in the literature only when the jumps are of finite variation. Here we give the speed even in presence of infinite variation jumps, as they appear e.g. in some cgmy plus diffusion models.

Suggested Citation

  • Cecilia Mancini, 2010. "Speed of convergence of the threshold estimator of integrated variance," Working Papers - Mathematical Economics 2010-03, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
  • Handle: RePEc:flo:wpaper:2010-03
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    References listed on IDEAS

    as
    1. Cecilia Mancini, 2009. "Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296, June.
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    Keywords

    Integrated variance; threshold estimator; convergence speed; infinite activity stable Le'vy jumps.;
    All these keywords.

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