English

Multifractal fluctuations in finance

Statistical Mechanics 2008-12-02 v1 Disordered Systems and Neural Networks Statistical Finance

Abstract

We consider the structure functions S^(q)(T), i.e. the moments of order q of the increments X(t+T)-X(t) of the Foreign Exchange rate X(t) which give clear evidence of scaling (S^(q)(T)~T^z(q)). We demonstrate that the nonlinearity of the observed scaling exponent z(q) is incompatible with monofractal additive stochastic models usually introduced in finance: Brownian motion, Levy processes and their truncated versions. This nonlinearity corresponds to multifractal intermittency yielded by multiplicative processes. The non-analycity of z(q) corresponds to universal multifractals, which are furthermore able to produce ``hyperbolic'' pdf tails with an exponent q_D >2. We argue that it is necessary to introduce stochastic evolution equations which are compatible with this multifractal behaviour.

Keywords

Cite

@article{arxiv.cond-mat/0102369,
  title  = {Multifractal fluctuations in finance},
  author = {F. Schmitt and D. Schertzer and S. Lovejoy},
  journal= {arXiv preprint arXiv:cond-mat/0102369},
  year   = {2008}
}

Comments

4 pages, 2 figures

R2 v1 2026-07-22T10:17:03.894Z