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

Author

Listed:
  • R. Fernández-Pascual
  • M. Ruiz-Medina
  • J. Angulo

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

Suggested Citation

  • R. Fernández-Pascual & M. Ruiz-Medina & J. Angulo, 2003. "Multiscale estimation of processes related to the fractional Black-Scholes equation," Computational Statistics, Springer, vol. 18(3), pages 401-415, September.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:3:p:401-415
    DOI: 10.1007/BF03354606
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    References listed on IDEAS

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    1. Calvet, Laurent & Fisher, Adlai, 2001. "Forecasting multifractal volatility," Journal of Econometrics, Elsevier, vol. 105(1), pages 27-58, November.
    2. Niels VÖver Hartvig & Jens Ledet Jensen & Jan Pedersen, 2001. "A class of risk neutral densities with heavy tails," Finance and Stochastics, Springer, vol. 5(1), pages 115-128.
    3. Ruiz-Medina, M. D. & Anh, V. V. & Angulo, J. M., 2001. "Stochastic fractional-order differential models with fractal boundary conditions," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 47-60, August.
    4. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
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