Multiscale estimation of processes related to the fractional Black-Scholes equation

R. Fernández-Pascual, M. Ruiz-Medina and J. Angulo

Computational Statistics, 2003, vol. 18, issue 3, 415 pages

Abstract: We consider a fractional-order differential equation involving fractal activity time to represent the stochastic behaviour of a log-price process of an underlying asset. The log-price process is defined in terms of fractional integration of the fractional derivative of Brownian motion on fractal time. A stable solution to the extrapolation and filtering problems associated is obtained in terms of covariance vaguelette functions (Angulo and Ruiz-Medina 1999). A simulation study is carried out to illustrate the methodology presented. Copyright Physica-Verlag 2003

Keywords: Brownian motion; Fractal activity time; Fractional-order differential models; Risk-adjusted process; Vaguelette functions (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/BF03354606

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