Rafał Kowalski (INP PAN)
Multiscale financial correlations in Ising-inspired agent-based models
The financial market is an example of a complex system with an enormous number of dependencies and intricate correlations between components. Analysis of such systems requires applying sophisticated mathematical tools, while its modelling using a traditional top-down approach is difficult. In this context, financial markets are similar to thermodynamic systems that can be quantitatively described and modelled using techniques applied in statistical physics. We demonstrate how to quantify nonlinear dependencies in financial time series using complex network and multifractal analysis techniques. Obtained multifractal spectra are broad and often reveal left-hand side asymmetry, indicating great complexity of analysed signals, while cross-fluctuations functions obey a power law over a large range of scales suggesting nonlinear cross-dependencies between financial assets. Next, we present an authorial, Ising-inspired agent-based model of the financial market, which combines local and global interactions, allowing generation of multifractal time series. Moreover, the framework incorporates multiple subsystems and facilitates modelling nonlinearly cross-correlated signals thereby enabling simulations of entire financial indices, which in turn has a lot of potential for practical applications.