Extreme value theory and neural network for catastrophic fall prediction: a study of year 2008-2009

Extreme value theory to a certain extent is successful in modelling extreme events as it assumes that outliers follow distribution other than normal. However, a mathematical model might not just be sufficient to predict extreme events. Nowadays, extreme events have become so common that investors' past experience of such situations takes over and plays important role in guiding collective behaviour during downturn. In this study, firstly extreme events are modelled using generalised extreme value (GEV) distribution. Secondly, past deviations from return levels obtained as quantile of GEV distribution and future risk of market falling below the same level are classified using perceptron network. Neural network is basically used to inculcate learning form past market movements to predict future. Trained network hence obtained is used for simulating monthly risk for catastrophic years 2008 and 2009. Comparison of actual and forecasted results indicates substantial improvement in market fall prediction.

[1]  Jon Danielsson,et al.  Value-at-Risk and Extreme Returns , 2000 .

[2]  Chakradhara Panda,et al.  Predicting Stock Returns , 2006 .

[3]  Anthony S. Tay,et al.  Multivariate Density Forecast Evaluation and Calibration In Financial Risk Management: High-Frequency Returns on Foreign Exchange , 1999, Review of Economics and Statistics.

[4]  C. Klüppelberg,et al.  A single number can't hedge against economic catastrophes , 1999 .

[5]  Mehmed Kantardzic,et al.  Data Mining: Concepts, Models, Methods, and Algorithms , 2002 .

[6]  Randall S. Sexton,et al.  Toward global optimization of neural networks: A comparison of the genetic algorithm and backpropagation , 1998, Decis. Support Syst..

[7]  Derek W. Bunn,et al.  Financial time series modelling with discounted least squares backpropagation , 1997, Neurocomputing.

[8]  B. Mandelbrot.  The Variation of Certain Speculative Prices , 1963 .

[9]  S. Ghosh,et al.  An application of a multiple neural network learning system to emulation of mortgage underwriting judgements , 1988, IEEE 1988 International Conference on Neural Networks.

[10]  Ramazan Gençay,et al.  High volatility, thick tails and extreme value theory in value-at-risk estimation , 2003 .

[11]  F. Longin.  The Asymptotic Distribution of Extreme Stock Market Returns , 1996 .

[12]  Mehmed Kantardzic,et al.  Data-Mining Concepts , 2011 .

[13]  R. Reiss,et al.  Statistical Analysis of Extreme Values-with applications to insurance , 1997 .

[14]  D. Hammerstrom,et al.  Neural networks at work , 1993, IEEE Spectrum.

[15]  S. Resnick,et al.  Extreme Value Theory as a Risk Management Tool , 1999 .

[16]  Peter J.G. Vlaar.  Value at risk models for Dutch bond portfolios , 2000 .

[17]  VaR - ein Maß für das extreme Risiko , 1998 .

[18]  A. McNeil,et al.  Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach , 2000 .

[19]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[20]  A. McNeil.  Extreme Value Theory for Risk Managers , 1999 .

[21]  Bernard Widrow,et al.  Neural networks: applications in industry, business and science , 1994, CACM.

[22]  W. Enders.  Applied Econometric Time Series , 1994 .

[23]  B. Brookes,et al.  Statistical Theory of Extreme Values and Some Practical Applications , 1955, The Mathematical Gazette.

[24]  Chris Brooks,et al.  A Comparison of Extreme Value Theory Approaches for Determining Value at Risk , 2005 .

[25]  Rudolf Kruse,et al.  Information fusion in the context of stock index prediction , 2001, Int. J. Intell. Syst..

[26]  Salih N. Neftçi.  Value at Risk Calculations, Extreme Events, and Tail Estimation , 2000 .

[27]  Michael Y. Hu,et al.  Neural network forecasting of the British pound/US dol-lar exchange rate , 1998 .

[28]  E. Gumbel.  Statistical Theory of Extreme Values and Some Practical Applications : A Series of Lectures , 1954 .

[29]  Patricia Jackson,et al.  Bank Capital and Value at Risk , 1997 .

[30]  P. Burridge,et al.  Value-at-risk: Applying the extreme value approach to Asian markets in the recent financial turmoil , 2000 .

[31]  F. Longin,et al.  From value at risk to stress testing : The extreme value approach Franc ß ois , 2000 .

[32]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[33]  M. Kosaka,et al.  Application Of Neural Network To Technical Analysis Of Stock Market Prediction , 2001 .

[34]  Achilleas Zapranis,et al.  Stock performance modeling using neural networks: A comparative study with regression models , 1994, Neural Networks.

[35]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.