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Multifractal fluctuations in finance | | F. Schmitt
; D. Schertzer
; S. Lovejoy
; | | Date: |
21 Feb 2001 | | Journal: | Int. J. Theor. Appl. Fin., 3, 3 (2000), 361-364 | | Subject: | Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn | | 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. | | Source: | arXiv, cond-mat/0102369 | | Services: | Forum | Review | PDF | Favorites | |
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