NONLINEAR DYNAMICS AND CHAOS IN FINANCIAL MARKET MODELS

Abstract

The analysis of financial markets has significantly developed throughout the last few decades shifting towards models of complexity, volatility clustering and unpredictability. One of the most significant components in this evolution is the use of nonlinear dynamics and chaos theory in financial market models which give an understanding of what appears to be random price changes and of the underlying deterministic patterns. The study examines the application of nonlinear dynamical systems and chaotic behavior in the modeling of financial markets, that is, foreign exchange, equity returns and commodity prices. The study is conducted using a combination of econometric tests, phase space reconstruction, the Lyapunov exponent estimation and the recurrence quantification analysis, to determine how much market time series are nonlinearly dependent and sensitive to initial conditions which are characteristic of chaotic systems. Prices of leading stock indices, forex pairs, and energy commodities of both major stock indices were compiled on a daily basis over 20 years. In addition to quantitative testing, the study combines a literature review of theoretical principles and simulation studies of simple nonlinear maps ( e.g. logistic map and Hénon map ) to demonstrate how simple nonlinear systems can produce complex behaviour similar to financial time series.