Computational methodology for modelling the dynamics of statistical arbitrage

Burgess, Neil (2000) Computational methodology for modelling the dynamics of statistical arbitrage. Doctoral thesis, University of London: London Business School.

Abstract

Recent years have seen the emergence of a multi-disciplinary research area known as "Computational Finance". In many cases the data generating processes of financial and other economic time-series are at best imperfectly understood. By allowing restrictive assumptions about price dynamics to be relaxed, recent advances in computational modelling techniques offer the possibility to discover new "patterns" in market activity. This thesis describes an integrated "statistical arbitrage" framework for identifying, modelling and exploiting small but consistent regularities in asset price dynamics. The methodology developed in the thesis combines the flexibility of emerging techniques such as neural networks and genetic algorithms with the rigour and diagnostic techniques which are provided by established modelling tools from the fields of statistics, econometrics and time-series forecasting. The modelling methodology which is described in the thesis consists of three main parts. The first part is concerned with constructing combinations of time-series which contain a significant predictable component, and is a generalisation of the econometric concept of cointegration. The second part of the methodology is concerned with building predictive models of the mispricing dynamics and consists of low-bias estimation procedures which combine elements of neural and statistical modelling. The third part of the methodology controls the risks posed by model selection and performance instability through actively encouraging diversification across a "portfolio of models". A novel population-based algorithm for joint optimisation of a set of trading strategies is presented, which is inspired both by genetic and evolutionary algorithms and by modern portfolio theory. Throughout the thesis the performance and properties of the algorithms are validated by means of experimental evaluation on synthetic data sets with known characteristics. The effectiveness of the methodology is demonstrated by extensive empirical analysis of real data sets, in particular daily closing prices of FTSE 100 stocks and international equity indices.