an innovative tool for financial decision making: the case of artificial neural networks

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An Innovative Tool for Financial Decision Making: The Case of Artificial Neural Networks

Douglas Wood and Bhaskar Dasgupta

Artificial Neural Networks (ANNs) may be seen as examples of a mathematical innovation, providing the latest technique in the toolkit of the financial economist for modelling financial applications. ANNs hold several advantages over earlier statistical and optimisation techniques. These are data driven networks, specially useful for real-time and critical applications using complex sets of data. This paper describes some examples of current applications in the financial economics area, then gives some idea about how to design and develop neural network applications. The research carried out thus far suggests that ANN models offer improved results in capturing the transitory and non-linear relationships within globalised financial markets.

Introduction

rtificial Neural Networks (ANNs) are A based on an emerging and challenging computational technology. They offer a new avenue to explore the dynamics of financial markets. Primarily offering pattern-recog-

Neural network nition capabilities, neural networks com- financial plement traditional approaches for support- innovations ing financial decision making and problem

solving. By focusing on patterns in data, ANN complement relationship- or rule-based approaches used by statistical analysis and artificial intelligence procedures. Their ability to model non-linear dynamics, to deal with "noisy" data and their adaptability are poten- tially useful for a wide range of financial decision making requirements. In recent years, numerous financial applications based on a neural network approach have been developed in areas such as commodities trading, bank failure assessment, credit rating, investment screening, and loan underwriting.

Reported connectionist or neural applications cover wide areas of interest such

as pattern recognition, pattern mapping, dealing with noisy data, pattern completion, associative loops, classification, scheduling, optimisation, diagnosis, signal processing, abstraction, process control, data segmen- tation, data compression, complex mapping, modelling of complex phenomena, machine vision and speech recognition. The aim in using neural networks in finance is not to replace traditional methods but to provide alternative and complementary tools. The aim of this paper is to provide some examples where neural network approaches can be employed and to give some pointers for developing and designing neural network applications in financial economics.

The basics of artificial neural networks1

An ANN is a network of many very simple processors ("units"), each possibly having a (small amount of) local memory. These processors are also commonly called as neurons. The units are connected by unidirectional communication channels ("connections"),

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which carry numeric (as opposed to symbolic) data. The units operate only on their local data and on the inputs they receive via the connections. The resulting design bears obvious similarities to the structure of human brains and sub components thereof and in parallel with human learning, neural networks are created by some sort of "training" rule whereby the weights of connections are adjusted on the basis of presented examples of "right" and "wrong". In other words, neural networks "learn" from example, just as children learn by example about the dis- tinction between dogs and other domestic animals. In some ways, the way a neural network performs is quite similar to that of ordinary linear regression. The major difference between linear regression and neural networks is that in the former, it is assumed that the relationship between inputs and outputs is linear in nature, while neural networks model the relationship between the inputs and outputs in a nonlinear way. Neural networks normally have great potential for parallelism, since the computations of the components are independent of each other. (See Appendix 1 for a mathematical treatment of the foundations of neural networks.) The independence of network components supports both generalisation and parallelism because of the failure of the relations is not critical to continuing performance.

In principle, ANNs can compute any computable function, i.e. they can do every- thing a normal digital computer can do. In practice, NNs are especially useful for mapping problems which are tolerant of some errors, have lots of example data available, but to which hard and fast rules can not easily be applied. Examples can be found in the case of credit card fraud detection, equity investment and so on. It follows that neural networks are interesting for people in many different disciplines.

Computer scientists who want to find out about the properties of non-symbolic information processing with neural nets and about learning systems in general. Engineers of many kinds who want to explore the capabilities of neural networks on many areas (e.g. signal processing) to solve their application problems. Cognitive scientists who view neural networks as a possible apparatus to describe models of thinking and consciousness (High-level brain function). Neuro-physiologists who use neural networks to describe and explore medium-

level brain function (e.g. memory, sensory system, motorics). Physicists who use neural networks to model phenomena in statistical mechanics and for a lot of other tasks. Biologists who use Neural Networks to interpret nucleotide sequences. In the humanities, neural networks can assist with a variety of classification and dating problems of the "who wrote Shake- speare" type. Economists who are interested in explain- ing financial and economics markets.

There is considerable overlap between the fields of neural networks and statistics. Statistics is concerned with data analysis. In neural network terminology, statistical infer- ence means setting the programme to "learn" and to generalise from noisy data. Most neural networks that can learn to generalise effectively from noisy data are similar or identical to statistical methods2. However, some neural networks are not concerned with data analysis (e.g., those intended to model biological systems) and have little to do with statistics. Some neural networks do not learn (e.g., Hopfield nets) and also have little to do with statistics. Some neural networks can learn successfully only from noise- free data (e.g., ART or the perceptron rule) and therefore would not be considered as statistical methods.

The following books give a good introduc- tory overview of the area: Aleksander, and Morton, (1990), McCord Nelson, and Illing- worth, (1990), and Wasserman, (1989). As far as software implementation is concerned, a number of packages are available for a variety of platforms: ranging from MS-DOS, Macin- tosh to UNIX. Prices of these also range from freewarelshareware to professional packages costing f 3,000. Descriptions of some freeware packages available on the Internet.

GENESIS 1.4.2 (GEneral NEural SImu- lation System) is a general purpose simulation platform which was developed to support the simulation of neural systems ranging from complex models of single neurons to simulations of large networks made up of more abstract neuronal components. Most current GENESIS applications involve realistic simulations of biological neural systems.3 Mactivation: A neural network simulator for the Apple Macintosh.4 Nevada Backpropagation (NevProp): NevProp is a free, easy-to-use feedforward backpropagation (multilayer perceptron) program. It uses an interactive character- based interface, and is distributed as C

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174 CREATIVITY A N D INNOVATION MANAGEMENT

source code that should compile and run on most platforms. (Precompiled execut- ables are available for Macintosh and

Win" is a shareware Neural Networks (NN) package for Windows 3.1. Win" incorporates a very user friendly interface with a powerful computational engine. W i n " is intended to be used as a tool for beginners and more advanced neural networks users, it provides an alternative to using more expensive and hard to use packages. Win" can implement feed forward multi-layered NN and uses a modified fast back-propagation for training, It has extensive on line help, has various neuron functions, and allows on the fly testing of the network performance and generalisation. All training parameters can be easily modified while Win" is training. Results can be saved on disk or copied to the clipboard. Supports plotting of the outputs and weight distribution.6

The following is a list of available com- mercial packages available along with their vendor details. Please note that these are not recommended in any way. It is recommended that readers carry out a proper cost benefit analysis of the various software packages available.

Name: nnlxnn, Company: Neureka ANS,

DOS.)~

Address: Klaus Hansens vei 3 lB, 5037 Solheimsviken, NORWAY. Phone: + 47-555441631 +47-55201548 Email: [email protected]. no Operating system: nn: UNIX or MS-DOS, xnn: UNIXIX-windows System requirements: lOMb HD, 2 Mb RAM, Approx. price: USD 2000.

Company: California Scientific Software Address: 10024 Newtown rd, Nevada City, CA, 95959 USA Phone,Fax: 916 478 9040,916 478 9041 Email: [email protected]. tek. com Operating system: DOS, Windows, Mac, System requirements: Uses XMS or EMS for large models (PCs only): Pro version, Approx. price: $195, $795 Name: Neuralworks Professional I1 Plus, Company: Neuralware Inc. Address: Pittsburgh, PA 15276-9910 Phone: (412) 787-8222, FAX: (412) 787-8220 Operating system: PC, Sun, IBM RS6000, Apple Macintosh, SGI, Dec, HP. System requirements: varies. PC:2MB extended memory+ 6MB Harddisk space. Approx. price: call (depends on platform)

Name: BrainMaker, BrainMaker Pro,

Name: NeuroForecaster(TM)/Genetica 3.1 Company Accel Infotech (S) Pte Ltd. Address: 648 Geylang Road, Republic of Singapore 1438; Phone: + 65-7446863; Fax: + 65-7492467, email: accel@solomon. technet.sg Requirements: For IBM PC 386/486 with mouse, or compatibles MS Windows 3.1, MS DOS 5.0 or above 4 MB RAM, 5 ME3 available hard disk space min, 3.5 inch floppy drive, VGA monitor or above, Math coprocessor recommended. Neuroforecaster 3.1 for Windows is priced at US$1199 per single user license. Comments: One of the dedicated software for forecasting financial markets. Neuro- Forecaster is a user-friendly neural network program specifically designed for building sophisticated and powerful forecasting and decision-support systems (Time-Series Forecasting, Cross-Sectional Classification, Indicator Analysis). Its user-friendly interface allows the users to build applications quickly, easily and interactively, analyse the data visually and see the results immediately. The following example applications are included in the package: Credit Rating - for generating the credit rating of bank loan applications, Stock market 6 monthly returns forecast, Stock selection based on company ratios, US$ to Deutschmark exchange rate forecast, US$ to Yen exchange rate forecast, US$ to SGD exchange rate forecast, Prop- erty price valuation, XOR - a classical problem to show the results are better than others, Chaos - Prediction of Mackey- Glass chaotic time series, Sine-Wave - For demonstrating the power of Rescaled Range Analysis and significance of window size. Name: Neuralyst Version 1.4; Company Cheshire Engineering Corporation. Address: 650 Sierra Madre Villa, Suite 201, Pasadena CA, 91107. Phone: 818-351-0209; Fax: 818-351-8645. Operating system: Windows or Macintosh running Microsoft Excel Spreadsheet, Neuralyst is an add-in package for Excel. Approx. price $195 for windows or Mac. Comments: A simple model that is easy to use.

There is one particular conference which is dedicated to Neural Networks and its applications to financial markets. This is an annual conference, in which latest applied papers are discussed. For more information, contact the NeuroForecasting Unit, London Business School, Sussex Place, London, UK. Until now, we have been discussing the basics of

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neural networks. In the next section, we shall explore some applications of neural networks in finance.

A survey of ANN applications in finance

The current research in this area falls into the following categories: General studies and Equity Markets, Foreign Exchange Markets, Bond Markets, Interest Rate Analysis, Credit Evaluation, Macro Economic Modelling, and Bankruptcy Prediction. These applications are examined with a listing of papers in each area with a brief description. Then a few comments are made on the neural network development procedure in the financial economics area.

General Studies (including Equity Markets): These studies fall under the general category, in which the study has explored different architecture’s of neural networks and have generally used stock market time series to apply these architecture’s and techniques. These studies concentrate mainly on equity markets, and relate to a varied sample of equities, ranging from individual company stock prices to predicting the stock indices. The horizon ranges from intraday to monthly. Table 1 gives some examples of applications and research carried out in this area.

Foreign Exchange: Foreign exchange rate prediction is quite difficult and the data horizon is generally of a very high frequency nature, intraday or daily data. Generally, the US dollar and its cross rates is used. Primarily three models are evaluated, the next period direction, the next period level, and finally the historical volatility is estimated. (See Table 2 . )

Credit Evaluation 6 Bankruptcy Prediction Models: Credit evaluation models take up from the statistical discriminant analysis function, in which there are only two outputs, success or failure. These models rely on using a large number of cases, and are based on the pattern recognition abilities of the neural networks. These models are one of the most successful neural network models in real world applications, specially for fraud detection, credit card evaluation and other similar applications. (See Table 3.)

Macroeconomic Modelling: Macroeconomic modelling is difficult, primarily due to data limitations. Macroeconomic data is mainly quarterly in nature, so to get the required/

recommended number of data points, it is necessary to take a very large data horizon, which means that stationary and regime change problems start to appear. Otherwise, in shorter horizon data, the performance of neural networks is good. (See Table 4.)

Futures and Options: Neural Network performance in modelling derivative instru- ments such as futures and options is promis- ing with a considerably better performance achieved as compared to normal, static closed form solutions. The major directions of this kind of modelling is to model the historical volatility, implied volatility’s and to determine derivative mispricing. (See Table 5.)

Bonds t3 Interest Rate Markets: These models are of two major types, the first which relates to rating of bonds, and secondly which relates to prediction of the level or volatility or yields of bonds or interest rate related securities. This section concentrated on the various types of neural networks as applied to various financial markets. In the final section, we comment on the mechanics of developing neural networks in financial markets. (See Table 6 . )

Model development techniques

Neural Networks are proving successful in modelling financial markets, but require considerable investment in development time and resources. Design takes up more than 60% of the time, with development and implementation the remaining time. The euphemism that a model is only as good as the inputs, is particularly true in terms of neural networks. It is vital to get a good set of inputs for a proper functioning model. Un- fortunately, there is no hard and fast rule for selecting model inputs. Consequently, trial and error processes are required. Some rules of thumb do exist though. Previous econo- metriclstatistical or operations research models provide good indicators of probable inputs. To determine the best transformation/ conversion of the inputs, standard statistical tests such as auto-correlation, linear regression, factor analysis and cross correlation function analysis are helpful. These standard statistical techniques help in determining the set of input variables which are the best descriptors of the desired output variable(s). Univariate approaches where previous values of the target variable are the entire input rely heavily on auto correlation, Auto Regressive Integrated Moving Average Process (ARIMA),

Credit evaluation - a neural

network SUCCeSS

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Table 1: General Studies (including Equity Markets)

Authods) Title of Research

Anthony, M. (1993) Antoniou, A. (1993) Barr, D.S.; Mani, G. (1993) Binks, D.L.; Allinson, N.M. (1991) Bulsari, A.B.; Saxen, H. (1993) Chang, C.F.; et. al. (1993) Cox, E. (1993) Der, R.; et. al. (1993) Der, R.; English, H. (1993) Edmonds, A. (1993)

Garavaglia, S. (1993) Garavaglia, S. (1993) Gerke, W.; Baun, S. (1993) Hawley, D.D.; et. al. (1990) Hoptroff, R.G. (1993)

Hsieh, C. (1993) Hsu, W.; Tenorio, M.F. (1992) Johnson, P.N. (1993) Jones, R.D.; et. al. (1990) Jurik, M. (1992) Jurik, M. (1992) LeBlanc, M.; Tibshirani, R. (1993) Margarita, S. (1992) Metzger, M.A.; Mitsumoto, K. (1991)

Ormerod, P. (1990) O’Sullivan, J.W. (1993) Otter, P. (1993)

Serrano-Cinca, C.; et. al. (1993)

Tan, C.; Tsoi, A. (1993)

Weigend, A. (1993) Wood & Dasgupta, 1994 Yoon, Y.; et al. (1993)

Designing Neural Networks and Computational Learning Theory. Non-Linear Behaviour of Financial Markets. Neural Nets in Investment Management: Multiple Uses. Financial Data Recognition and Prediction Using Neural Networks. A Recurrent Neural Network for Time-Series Modelling. Multi-layered Back-Propagation Neural Networks for Finance Analysis. A Model Free Trainable Fuzzy System for the analysis of Financial Time Series Data. Prediction of Financial Time Series Using Hierarchical Self-organized Feature Maps. Prediction of Financial Time Series Using Hierarchical Self-organized Feature Maps. Multivariate Prediction of Financial Time Series Using Recent Developments in Chaos Theory. Desperately Seeking Stability: Neural Networks with Insufficient Data. Interpreting Neural Network Output. Neural Networks in Financial Forecasting - How to develop forecasting models. Artificial Neural Systems: A New Tool for Financial Decision Making. The Principles and Practice of Time Series Forecasting and Business Modelling Using Neural Nets. Some Potential Applications of Artificial Neural System in Financial Management. A Similarity-Based Approach to Forecasting. A Case-Based Reasoning Paradigm for Mining Financial Databases. Function Approximation and Time Series Prediction with Neural Networks. Trading Techniques: The case and feeding of a neural network. Going fishing with a neural network. Combining estimates in regression and classification. Genetic Neural Networks for Financial Markets: Some Results. Forecasting Multivariate Time-Series: Confidence Intervals and Comparison of Performances of Feed-Forward Neural Network and Statespace Models. Futures Issues: Chaotic Systems and Neural Networks in the Planning Process. Neural Nets - A Practical Primer or . . . What I wished I knew Four Years Ago. Feedforward Neural Network and Canonical Correlation Models as Approximators with an Application to One Year Ahead Forecasting. Topology-Preserving Neural Architectures and Multidimensional Scaling for Multivariate Data Analysis. Financial Time Series Forecasting with Recurrent Artificial Neural Network Techniques. Predicting the Future and Understanding the Past Behaviour. Global Portfolio Management, Modelling the Dynamics of MSCI Country Indices. A Comparison of Discriminant Analysis Versus Artificial Neural Networks.

Cassetti, M.D. (1993) Chinetti, D.; et. al. (1993) Cox, E. (1993) Deboeck, G.J. (1992) Deboeck, G.J. (1993) Grudnitski, G.; Osburn, L. (1993) Haefke, C. (1993)

Hiemstra, Y. (1993)

Hruschka, H. (1993)

Jang, G.; Lai, F. (1993)

Equity Markets A Neural Network System for Reliable Trading Signals. A Neural Network Model for Stock Market Prediction. Detecting Anomalous Risk behaviours in Portfolio Management Strategies. Pre-processing and evaluation of neural nets for trading stocks. Neural, Genetic, and Fuzzy Approaches to Design of Trading Systems. Forecasting S & P and Gold Futures Prices: An Application of Neural Networks. Results of a Simple Trading Scheme Based on an Artificial Neural Network on the Austrian Stock Market. A Neural Net to Predict Quarterly Stock Market Excess Returns Using Business Cycle Turning Points. Determining market response functions by neural networks modeling: A comparison to econometric techniques. Intelligent Stock Market Prediction System using Dual Adaptive-Structure Neural Networks.

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Kryzanowski, L.; et. aL(1993) Lee, D.; Tiam, L. (1993) McCluskey, P.C. (1993)

Meir, D.; Pfeifer, R. (1993) Papadourakis, G.; et. al. (1993) Refenes, A,; Zapranis, A. (1993) Schumann, M.; Lohrbach, T. (1993)

Steiner, M. (1993) Swales, G.S.; Yoon, Y. (1992) Tanigawa, T.; Kamijo, K. (1992) White, H. (1987) Wong, F.; Lee, D. (1993) Wong, F.S.; et. al. (1992)

Using Artificial Neural Networks to pick Stocks. Hybrid Technologies for Far East Markets. Feedforward and Recurrent Neural Networks and Genetic Programs for Stock Market and Time Series Forecasting. Is Mean-Reversion on Stock Indices a Linear Effect? Application of Neural Networks in Short Term Stock Price Forecasting. Using Neural Networks for Modelling the French Stock Market. Comparing Artificial Neural Networks with Statistical Methods within the field of Stock Market Prediction. Neural Networks as an Alternative Market Model. Applying Artificial Neural Networks to Investment Analysis. Stock Price Pattern Matching System. Economic Prediction Using Neural Networks: The Case of IBM Daily Stock Returns. Hybrid Neural Networks for Stock Selection. Fuzzy Neural Systems for Stock Selection.

Table 2: Foreign Exchange

Author(s)

Abu-Mustafa, Y. (1993)

Garliauskas, A,; Garliauskiene, A. (1993) Pi. H. (1993) Poddig, T. (1993) Refenes, A.N.; et. al. (1993) Wurtz, D.; et. al. (1993)

Title of Research

Nonparametric Exchange Rate Prediction by using a Modified Nearest Neighbour Method. Novel Neural Networks in a prediction for Foreign Exchange Rates. Dependency Analysis and Neural Networks Modelling of Currency Exchange Rates. Short Term Forecasting of the USDIDM-Exchange Rate. Currency Exchange Rate Prediction and Neural Network Design Strategies. A "Neural" Decision Support System for Predicting Currency Exchange Rates.

Table 3: Credit Evaluation & Bankruptcy Prediction Models

A u t h or (s) Title of Research

Baestaens, D.; et. al. (1993) Jost, A. (1993) Yamamoto, Y.; Zenios, S.A. (1993)

Ballarin, A.; Daniele, M. (1993) Ballarin, A.; et. al. (1993) Fletcher, D.; Goss, E. (1993)

Qualitative Credit Assessment Using a Neural Classifier. Neural Networks: A logical progression in credit and marketing decision making. Predicting Prepayment Rates for Mortgages using the Cascade Correlation Learning Algorithm. Corporate Bankruptcy Forecast using CERVED Financial and Economic Databases. Forecasting Corporate Bankruptcy: A Neural Network Approach. Forecasting with Neural Networks: An application using bankruptcy data.

Table 4: Macroeconomic Modelling

Author(s) Title of Research -

Baestaens, D.; Van den Bergh, W. (1993) Baestaens, D.; Van den Bergh, W. (1991) Biggs, N. (1993) Moody, J. (1993) Trigueiros, D. (1993) Wong, F.; Tan, P.Y. (1993)

Estimating Tax Inflows at a Public Institution. Pattern Recognition Devices as a support to Financial Economic Decision-Making. Economic Forecasting with Neural Nets: a Computational Learning Theory. Macroeconomic Forecasting with Neural Networks. A Taxonomy of Risk in Large UK Industrial Firms. Neural Networks and Genetic Algorithms for Economic Forecasting.

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Table 5: Futures and Options

Author($ Title of Research

Bailey, D.L.; et. al. (1988) Grutniski, G. (1993) Hutchinson, J.M.; et. al. (1994)

Kat, H.M. (1992) Kingdon, J. (1993)

Miranda, F. (1993) Refenes, A. (1993) Trippi, R.R.; DeSieno, D. (1992)

Options Trading using Neural Networks. Important Factors in Neural Networks - Forecasts of Gold Futures Prices. A nonparametric approach to pricing and hedging derivative securities via learning networks. Modeling S&P 500 Futures Mispricing using a neural network. Neural Nets for Time Series Forecasting: Criteria for Performance with an Application in Gilt Futures Pricing. Estimation of Implied Volatilities Using a Neural Network Approach. Neural Networks for Financial Engineering. Trading Equity Index Futures with a Neural Network: A machine learning-enhanced strategy.

Table 6: Bonds 6 lnterest Rate Markets

Author($ Title of Research

Barone, E.; et, al. (1993)

Bilge, U.; Refenes, A. (1993) Dutta, S.; Shekhar, S. (1988) Dutta, S.; Shekhar, S. (1992) Moody, J. (1993) Singleton, J.; Surkan, A. (1993) Utans, J.; Moody, J. (1991)

Landi, L.; Barucci, E. (1993)

Forecastability of Returns with Neural Networks: An Application to Spot and Futures Italian Bond Markets. Application of Sensitivity Analysis Techniques to Neural Network Bond Forecasting. Bond Rating: A Non-Conservative Application of Neural Networks. Generalization with Neural Networks: An application in the financial domain. Bond Rating using Neural Networks. Bond Rating with Neural Networks. Selecting Neural Network Architectures via the Prediction Risk: Application to Corporate Bond Rating Prediction. Artificial Neural Networks for Treasury Bills Rate Forecasting.

and Auto Regressive Conditional Hetero- scedascity (ARCH) techniques to determine the best explanation. These univariate models rely on a fundamental assumption that the information contained in the past values of the time series can be used to predict the future. The autocorrelation technique tells us as to whether there is a relationship between today's values and past values. This helps to develop models such as ARIMA models which model the time series as a function of moving averages within a regression frame- work. ARCH models are based on modelling time series volatility as a function of past mean and deviations from this mean.

Once a set of inputs and outputs has been decided upon, the next step is to determine the architecture of the neural network. This involves in deciding the number of hidden layers (i.e. layers between inputs and ob- served outputs), the number of nodes on each layer (connections), and the basic algorithm to be used. Generally in financial

applications, we find that the BackPropa- gation-Feedforward algorithm is most commonly used. Increasing the complexity of the model in terms of layers and nodes is possible with networks of more than 25 inputs, 25 outputs and two hidden layers with more than 30 hidden nodes have been reported. To determine the number of hidden layers, some rules of thumb have been reported such as dividing the number of inputs plus the number of outputs by two but there is no hard or fast rule about the architecture, a trial and error mechanism has to be adopted and is almost totally dependent on the type of application and data mechanics. For a simple credit evaluation model, 5-10 inputs, one hidden layer with 3-5 neurons and one output can be acceptable, on the other hand, an options trading model may require a complex model.

There is another aspect to be noted in neural network development. This is the number of cases or data points to be used.


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There are lots of rules-of-thumb for this. For example, a very common rule of thumb is that the number of data points has to be 10 times the number of weights andlor connections. So for a small model, the required number of cases could be 1000, although, good results have been reported using just 100 cases for a network which has about 40 weightslconnections. Generally, a minimum of 500-1000 cases are required for a good model which is robust in terms of out of sample performance.

The final aspect to be considered is the implementation aspect. NN models have the advantage of continuous learning so they have to be set up so that they are “trained” every period. Another good strategy is to have a strategy of continuous improvement, so that, say for a daily model, it is re-evaluated every three or six months, if there is no major regime change in the intervening period. O n the other hand, the model should be checked after every major regime change such as a stock market crash, psychological barriers such as Yen 100 to the US Dollar, 3000 level for the FTlOO etc. This concludes our overview and model development techniques for using neural networks in financial economics. Properly designed, these models are capable of excellent and robust performance, specially when compared to other alternatives such as econometricloperations research or statistical models.

Conclusions

The world has seen massive deregulation in recent years. Not surprisingly attempting to model financial markets using rule-type models which track regulatory constraints proved fragile; whereas NN approaches which let data determine structure and are capable of ”learning” are more robust. Neural Networks which trace back what does happen in the market to what might have caused it, have an advantage compared with models that observe fundamentals and then predict consequences. Neural networks re- flect that in a computer age, non-linear models, drawing on multidimensional inputs are just as likely to be important as the use of linear trends in understanding markets.

Notes

1. The source for this section is the Neural Network Frequently Asked Questions (FAQ) List, which is issued on a bimonthly frequency on the USENET newsgroup comp.ai.neura1-nets, maintained by

2.

3.

4.

5.

6.

Lutz Prechelt, prechelt @ ira. uka. de; URL: : http: I/wwwipd.ira.uka.de/ - precheltlFAQ1 neural-net-faq. html. An electronic version of the file can be accessed from the given URL (Uniform Resource Locater). Feedforward nets with no hidden layer (including functional-link neural nets and higher-order neural nets) are basically generalised linear models, Feedforward nets with one hidden layer are closely related to projection pursuit regression, Probabilistic neural nets are identical to kernel discriminant analysis, Kohonen nets for adaptive vector quantization are very similar to k-means cluster analysis, Hebbian learning is closely related to principal com- ponent analysis etc. Contact: [email protected]. Further information via WWW at http:llwww. bbb.caltech.edulGENESIS1 Available for ftp from ftp.cs.colorado.edu [128.138.243.151] as IpublcslmiscIMactivation- 3.3. sea. hqx The most updated version of NevProp will be made available by anonymous ftp from the Uni- versity of Nevada, Reno: On ftp.scs.unr.edu [134.197.10.130] in the directory ”publgoodman Inevpropdir”. Limited support is available from Phil Goodman ([email protected]), Univer- sity of Nevada Center for Biomedical Research. Available for ftp from winftp.cica.indiana.edu as Ipublpclwin3lprogramrlwinnn093. zip(545 kB).

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Anthony, M. (1993): Designing Neural Networks and Computational Learning Theory. Proceed- ings of the First International Workshop on Neural Networks in the Capital Markets, London.

Antoniou, A. (1993): Non-Linear Behaviour of Financial Markets. Proceedings of the First Inter- national Workshop on Neural Networks in the Capital Markets, London.

Baestaens, D. and Van den Bergh, W. (1993): Qualitative Credit Assessment Using a Neural Classifier. Proceedings of the First International Workshop on Neural Networks in the Capital Markets, London.

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Baestaens, D.E. and Van den Bergh, W.M. (1991): Pattern Recognition Devices as a support to Financial Economic Decision-Making. Working Paper Series, Erasmus Centre for Financial Re- search, Rotterdam 9105, 1-30.

The impOrtUnCe Of non-linear models


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Ballarin, A. and Daniele, M. (1993): Corporate Bankruptcy Forecast using CERVED Financial and Economic Databases. Corporate Credit Management Seminar, London 1, 1-9.

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Appendix 1: A Mathematical Introduction to Neural Networks

Artificial Neural Networks are data driven methods generally built around non-linear activation (squashing) functions (or non- linear transfer functions). These networks are allowed to determine the non-parametric dynamics of the indices with minimal assumptions on the indices. The inputs are mapped on to the output after being transformed through a squashing function (generally sigmoid in nature), this mapping is generally non-linear in nature although they are also capable of dealing with ARIMA like models, Bulsari & Saxen (1993) give an excellent description of how these learning networks can be used to approximate and model ARIMA models. Non-parametric models offer some major advantages over traditional parametric methods. Firstly as they do not force restric-


183

tive parametric assumptions such as log- normality or sample-path continuity and they tend to be robust to the specification errors that plague parametric models. Second, they are adaptive and respond to structural changes in the data generating processes in ways that parametric models could only approximate with ad-hoc procedures and finally they are flexible enough to implement and cater for a wide range of input vectors and high dimensionality. For example, Hutchin- son et. al. (1994) report when modelling the Black Scholes model, the entire learning network becomes the model itself.

Generally, for prediction of time series, two functions are normally used, logistic activation giving rise to sigmoid transfer functions (a.k.a. multi layer perceptrons) and the other is Gaussian activation giving rise to radial basis transfer functions, Weigend et al. (1990). For sigmoid functions, let ln denote the input vector including a bias bh into a sigmoid or logistic hidden unit h, so

d

i = l [ h = c W h i X i + b h = z h @ f + b h

where, xi stands for xt-i, the time series xt, the value of input i, and Whj is the parameter/ weight between input unit i and the hidden unit h. The contribution fih@f'is the projection of the input vector f= (xl,x2,. . . . . . .,xd) on

activation s h of the hidden unit is then

Sh=S(t$h)=- 1 -- -1 (l+tanh:[h)

the weight Vector fh=( (xh l ,Xhz , ......., Xhd). The

I + e - " ' h

This sigmoid function performs a smooth mapping, ( - 00, + m)+(O, 1). The slope of

the sigmoid can be absorbed into the weights and biases without loss of generality and is set to one. The Radial Basis Function depends only on the distance 7 = 11 f- ph 11 between the input f a n d the centre of the function Fh also of input dimension d, so d(x' )= +( IIf-Fh 11) = $(q) , choosing f to be Gaussian and I( 1) to be the Euclidean norm, the activation Gh of the hidden unit h is given by

the standard deviation represents the width of the Gaussian, and the normalisation of Gaussian radial basis function would be between zero and one. Maruyama, et. al. (1991) show that there is no difference between the radial basis functions and the multilayer perceptrons when normalised inputs are used in multilayer perceptrons. In the world of financial applications, we find that these are the two most commonly used methodologies used to model financial data.

Douglas Wood is National Westminster Bank Professor of Banking and Corporate Finance at Manchester Business School, Manchester, UK Bhaskar Dasgupta is a doctoral researcher at Manchester Business School, Manchester, UK


an innovative tool for financial decision making: the case of artificial neural networks

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