We demonstrate how the basic ideas of the fractal and the heterogeneous mar
ket hypotheses lead to a rigorous mathematical model, which can be used to
solve the problem of characterizing the distribution of price changes corre
sponding to the empirical scaling law of volatility for high-frequency data
from the foreign exchange market. For this purpose, we adopt the condition
ally exponential decay model, which describes asymptotic behaviour of gener
al complex systems. We also discuss the overall rationale for why one might
expect such scaling laws to hold for financial data. (C) 1999 Elsevier Sci
ence B.V. All rights reserved.