A conditionally exponential decay approach to scaling in finance

We demonstrate how the basic ideas of the fractal and the heterogeneous market hypotheses lead to a rigorous mathematical model, which can be used to solve the problem of characterizing the distribution of price changes corresponding to the empirical scaling law of volatility for high-frequency data from the foreign exchange market. For this purpose, we adopt the conditionally exponential decay model, which describes asymptotic behaviour of general complex systems. We also discuss the overall rationale for why one might expect such scaling laws to hold for financial data.