New Views on Forecasting and Risk based on Large Recurrent Neural Networks

Quant Talk
Wednesday, 28 October 2009
6.30 pm, room 21

Abstract

In the age of globalization, extensive deregulations and considerable developments in information technology, financial markets are highly interrelated. Segregated market analyses which are often performed in econometrics or in technical studies of market actions are therefore questionable. What is required is a joint modeling of all interrelated markets. We have developed large time-delay recurrent neural networks that model coherent markets as interacting dynamical systems.

Large recurrent neural networks are formulated as nonlinear state space models. These models combine different operations of small neural networks (e.g. processing of input information) into only one shared state transition matrix. We use unfolding in time to transfer the network equations into a spatial architecture. The training is done with error backpropagation through time.

Large networks are over-parameterized (even beyond the point of a perfect modeling). Unlikely to standard econometric techniques, the under-determination of the large networks creates an eigen-noise which prevents overfitting and the associated loss of generalization abilities. The self-created eigen-noise can also be interpreted as the impact of hidden variables of the system dynamics. Given a finite number of observations for the considered market dynamics, there are many different scenarios for the reconstruction of the hidden variables. These scenarios result in a diversifying out-of-sample behavior. One of the scenarios is the true dynamics – but we do not know which one! Thus, we take the average of the ensemble as the expected forecast. The ensemble distribution can be seen as a measure of risk.

We have applied large neural networks to forecast the development of the Dow Jones Industrial Average stock index. Here we us the ensemble distribution for the valuation of corresponding options and derive appropriate trading strategies