Pointwise Regularity Exponents and Market Cross-Correlations

The multifractional Brownian motion is a locally dependent Gaussian nonstationary process, whose flexibility in describing complex phenomena justifies its use in financial dynamics modeling. Assuming it as a model of stock indexes, we estimate the pointwise regularity function for the Dow Jones Ind. Avg., the Footsie 100 and the Nikkei 225. We also analyze the pairwise cross-correlation of the functions themselves and compare them with the pairwise cross-correlation of log variations