Could nonlinear dynamics contribute to intra-day risk management?

Abstract

We use techniques drawn from the field of nonlinear dynamics, often popularly referred to as chaos theory, to study high frequency (tick by tick) time series of foreign exchange and interest rates. The existence of strange attractors is extensively investigated by applying the nearest-neighbours algorithm for the computation of fractal dimensions to the signals reconstructed with the time-delay embedding technique. Furthermore, the state space reconstruction allows us to test whether, in the course of a business day, forecasts based on this technique could improve the timing of hedge trades, in the foreign exchange and interest rate markets. We find that this approach does not reduce hedging costs. This casts strong doubts on the ability of nonlinear dynamics to be of any practical use in financial risk management.