Fractional calculus and continuous-time finance

Details Fractional calculus and continuous-time finance Fractional calculus and continuous-time finance

2000-01-10

arxiv.org/abs/cond-mat/0001120v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, no figures, LaTeX2e, submitted to Physica A

Scientific paper

10.1016/S0378-4371(00)00255-7

In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the L\'evy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predictions on the long-time behaviour of the waiting-time probability density are presented. Finally, a general scaling form is given, based on the solution of the fractional diffusion equation.

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