Summary
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.
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Acknowledgments
This work has been supported in part by projects BFM2000-1465 and BFM2002-01836 of the DGI, Spain.
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Fernández-Pascual, R., Ruiz-Medina, M.D. & Angulo, J.M. Multiscale estimation of processes related to the fractional Black-Scholes equation. Computational Statistics 18, 401–415 (2003). https://doi.org/10.1007/BF03354606
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DOI: https://doi.org/10.1007/BF03354606