Genetic Algorithms and Genetic Programming in Computational Finance

This chapter reviews some recent advancements in financial applications of genetic algorithms and genetic programming. We start with the more familiar applications, such as forecasting, trading, and portfolio management. We then trace the recent extensions to cash flow management, option pricing, volatility forecasting, and arbitrage. The direction then turns to agent-based computational finance, a bottom-up approach to the study of financial markets. The review also sheds light on a few technical aspects of GAs and GP, which may play a vital role in financial applications.

After a brief overview of the history of the development and application of genetic algorithms and related simulation techniques, this chapter describes alternative implementations of the genetic algorithm, their strengths and weaknesses. Then follows an overview of published applications in finance, with particular focus on the papers of Bauer, Pereira, and Colin in foreign exchange trading. Many other rumored applications remain unpublished.

This chapter demonstrates a computer program for tutoring genetic programming (GP). The software, called Simple GP, is developed by the AI-ECON Research Center at National Chengchi University, Taiwan. Using this software, the instructor can help students without programming background to quickly grasp some essential elements of GP. Along with the demonstration of the software is a list of key issues regarding the effective design of the implementation of GP. Some of the issues are already well noticed and studied by financial users of GP, but some are not. While many of the issues do not have a clear-cut answer, the attached software can help beginners to tackle those issues on their own. Once they have a general grasp of how to implement GP effectively, many advanced materials prepared in this volume are there for further exploration.

This paper investigates the predictive power of the volume of messages produced on internet stock-related measure boards. We introduce a specialized GP learner and demonstrate that it produces trading rules that outperform appropriate buy and hold strategy benchmarks in measures of risk adjusted returns. We compare the results to those attained by using other relevant variables, lags of price and volume, and find that the the message board volume produces cleraly superior results. We experiment with alternative representations for the GP trading rule learner. Finally, we find a potential regime shift in the market reaction to the message volume data, and speculate about future trends.

This paper addresses the problem of finding trends in financial data series using genetic programming (GP). A GP system STROGANOFF that searches for polynomial autoregressive models is presented. The system is specialized for time series processing with elaborations in two aspects: 1) preprocessing the given series using data transformations and embedding; and, 2) design of a fitness function for efficient search control that favours accurate, parsimonious, and predictive models. STROGANOFF is related to a traditional GP system which manipulates functional expressions. Both GP systems are examined on a Nikkei225 series from the Tokyo Stock Exchange. Using statistical and economical measures we show that STROGANOFF outperforms traditional GP, and it can evolve profitable polynomials.

In this chapter, a hybrid approach for stock market forecasting is presented. It allows to develop a mixture of hybrid experts, each consisting of a genetic classifier and an associated artificial neural network. The resulting experts have been applied to stock market forecasting using technical trading rules as genetic inputs and other inputs—in particular past quotations—for the neural networks. In particular, the former are used to find quasi-stationary regimes within the financial data series, whereas the latter are assigned the task of making “context-dependent” predictions on the next day trend of the market. To this end, a novel kind of feedforward artificial neural network has been defined, allowing to implement suitable predictors without being compelled to exploit more complex neural architectures. Test runs have been performed on some well-known stock market indexes, also taking into account trading commissions. The tests pointed to the good forecasting capability of the proposed approach, which repeatedly outperformed the buy-and-hold strategy.

EDDIE is a genetic-programming based system for channelling expert knowledge into forecasting. FGP-2 is an implementation of EDDIE for financial forecasting. The novelty of FGP-2 is that, as a forecasting tool, it provides the user with a handle for tuning the precision against the rate of missing opportunities. This allows the user to pick investment opportunities with greater confidence.

This study examines the potential of an evolutionary automatic programming methodology, Grammatical Evolution, to uncover a series of useful technical trading rules for market indices. A number of markets are analysed; these are the UK’s FTSE, Japan’s Nikkei, and the German DAX. The preliminary findings indicate that the methodology has much potential.

Technical indicators are developed for monitoring the movement of stock prices from different perspective. They are widely used to define trading rules to assist investors to make the buy-sell-hold decision. Most of these trading rules are vague and fuzzy in nature. Since the stock prices are affected by the artificial news factors from time to time, investors cannot be the winner all the time on using the same set of trading rules. The weight (i.e., the significance) of a trading rule to investors is varying with time. The problem of determining the weight of the trading rules can be modelled as an optimization problem. In this paper, we propose a Genetic Fuzzy Expert Trading System (GFETS) for market timing. We apply the fuzzy expert system to simulate vague and fuzzy trading rules and give the buy-sell signal. The set of trading rules adopted in the system will vary with time and is optimized using Genetic Algorithm (GA). Two training approaches—incremental and dynamic—are designed and studied. The system was evaluated with the stocks in NASDAQ market. Experimental results showed that the system can give reliable buy-sell signals and using the system to perform buy-sell can produce significant profit.

This paper presents the development of a hybrid system based on Genetic Algorithms, Neural Networks and the GARCH model for the selection of stocks and the management of investment portfolios. The hybrid system comprises four modules: a genetic algorithm for selecting the assets that will form the investment portfolio, the GARCH model for forecasting stock volatility, a neural networks for predicting asset returns for the portfolio, and another genetic algorithm for determining the optimal weights for each asset. Portfolio management has consisted of weekly updates over a period of 49 weeks.

This article describes an intelligent system for financial planning and cash flow optimization, designed and developed by PUC-Rio (Pontifícia Universidade Católica do Rio de Janeiro) for the Souza Cruz, Brazilian tobacco company. The system, named ICF: Intelligent Cash Flow, is a computational tool for decision making support which provides short-term and long-term financial managing strategies, considering financial products of the market. The ICF makes use of Genetic Algorithms, a search and optimization technique inspired in natural evolution and the genetics, in order to elaborate plannings and cash flow projections which offer more profitability and liquidity for the considered period. From the planning alternatives offered by the system, the user can decide each day the investment and resource allocation options that suit better the demands and policy of the firm. The ICF analyses 500.000 different planning options in 20 minutes in order to identify the most profitable cash flows.

In this paper, we use Genetic Programming, an optimization technique based on the principles of natural selection, to price financial contingent claims. Compared to the traditional arbitrage-based approach, this technique is useful when the underlying asset dynamics are unknown or when the pricing equations are too complicated to solve analytically. Comparing to other established data-driven option pricing techniques such as neural networks, implied binomial trees, etc., genetic programming has the advantage of not restricting the structure of the pricing formulas. In addition, because it is very easy to incorporate existing analytical pricing formulas into the evolutionary process, genetic programming can be applied in combination with existing pricing methods. In this paper, we show that genetic programming can recover Black-Sholes formula from a simulated data sample of fairly small size. The application to S&P 500 futures options also show promising results.

This article illustrates the strengths and weaknesses of genetic programming in the context of forecasting out-of-sample volatility in the DEM/USD and JPY/USD markets. GARCH(1,1) models serve used as a benchmark. While the GARCH model outperforms the genetic program at short horizons using the mean-squared-error (MSE) criterion, the genetic program often outperforms the GARCH at longer horizons and consistently returns lower mean absolute forecast errors (MAE).

EDDIE-ARB (EDDIE stands for Evolutionary Dynamic Data Investment Evaluator) is a genetic program (GP) that implements a cross market arbitrage strategy in a manner that is suitable for online trading. Our benchmark for EDDIE-ARB is the Tucker (1991) put-call-futures (P-C-F) parity condition for detecting arbitrage profits in the index options and futures markets. The latter presents two main problems, (i) The windows for profitable arbitrage opportunities exist for short periods of one to ten minutes, (ii) Prom a large domain of search, annually, fewer than 3% of these were found to be in the lucrative range of £500-£800 profits per arbitrage. Standard ex ante analysis of arbitrage suffers from the drawback that the trader awaits a contemporaneous signal for a profitable price misalignment to implement an arbitrage in the same direction. Execution delays imply that this naive strategy may fail. A methodology of random sampling is used to train EDDIE-ARB to pick up the fundamental arbitrage patterns. The further novel aspect of EDDIE-ARB is a constraint satisfaction feature supplementing the fitness function that enables the user to train the GP how not to miss opportunities by learning to satisfy a minimum and maximum set on the number of arbitrage opportunities being sought. Good GP rules generated by EDDIE-ARB are found to make a 3-fold improvement in profitability over the naive ex ante rule.

The paper presents an extended version of the standard textbook problem of consumer choice. As usual, agents have to decide about their desired quantities of various consumption goods, at the same time taking into account their limited budget. Prices of the goods are not fixed but arise from a Walrasian interaction of total demand and a stylized supply function for each of the goods. After showing that this type of model cannot be solved analytically, three different types of evolutionary algorithms are set up to answer the question whether agents’ behavior according to the rules of these algorithms can solve the problem of extended consumer choice. There are two important answers to this question: a) The quality of the results learned crucially depends on the elasticity of supply, which in turn is shown to be a measure of the degree of state dependency of the economic problem. b) Statistical tests suggest that for the agents in the model it is relatively easy to adhere to the budget constraint, but that it is relatively difficult to reach an optimum with marginal utility per Dollar being equal for each good.

This paper examines the behavior of price discovery within a context of an agent-based artificial stock market. In this model, traders stochastically update their forecasts by searching the business school whose evolution is driven by genetic programming. We observe how well the market can track the “true price” i.e., the homogeneous rational expectations equilibrium price (HREEP). It is found that market prices are statistically significantly biased. Furthermore, the pricing error is negatively correlated to market size. Excess volatility is also noticeable in these markets.

In this chapter we conduct two experiments within an agent-based double auction market. These two experiments allow us to see the effect of learning and smartness on price dynamics and allocative efficiency. Our results are largely consistent with the stylized facts observed in experimental economics with human subjects. From the amelioration of price deviation and allocative efficiency, the effect of learning is vividly seen. However, smartness does not enhance market performance. In fact, the experiment with smarter agents (agents without a quote limit) results in a less stable price dynamics and lower allocative efficiency.

In this paper we test computationally the performance of CAPM in an evolutionary setting. In particular we study the stability of distribution of wealth in a financial market where some traders invest as prescribed by CAPM and others behave according to different portfolio rules. Our study is motivated by recent analytical results that show that, whenever a logarithmic utility maximiser enters the market, CAPM traders vanish in the long run. Our analysis provides further insights and extends these results. We simulate a sequence of trades in a financial market and: first, we address the issue of how long is the long run in different parametric settings; second, we study the effect of heterogeneous savings behaviour on asymptotic wealth shares. We find that CAPM is particularly “unfit” for highly risky environments.

The problem of time series prediction is transformed into one of pattern recognition with rule extraction under the framework of genetic algorithm. The time series is digitized into an ordered sequence of alphabets representing different classes of fluctuation by standard signal processing techniques. The problem of forecasting financial time series is then mapped into one of classification of the daily rate of return. Results obtained on real as well as artificial time series indicate that genetic algorithm is a useful method for forecasting. These applications were also modeled in the context of multi-agent system, where each agent represents an adaptive portfolio manager who has a particular rule of prediction. These portfolio managers will be supplemented with certain human characters, such as a level of greed and fear, so that they will have different behaviors in their investment strategies. Group of investors form team that possesses certain average view on the market defined by the conventional wisdom of the team members. The effects of this collective view, which can be first taken as a source of random news, are incorporated via a model of herd effect to characterize the human nature of the investors in changing their original plan of investment when the news contradicts their prediction. Evolution of the net asset value of the teams, as a prototype of fund house, is monitored and discussed in terms of the general human characters assigned to the team members. The transactions taken by each team member are recorded and the decision process in the switching of assets is modelled with different level of sophistication. A universal feature that greedy and confident investors outperform others emerges from this study. A general discussion that relates the consistency of performance, rate of increase of net asset and the human nature in the decision process is made.

This paper investigates the performance of a number of variants of the GA within the context of the OLG model of Bullard and Duffy (1999), in which a GA is used to model a population of agents adjusting their heterogeneous beliefs about future prices. Bullard and Duffy found the population converged onto the Pareto superior equilibrium in the model. A number of experiments and analysis suggest this is a robust result. The paper also introduces a meta-learning model in which agents learn to learn. In this meta-learning model each agent uses an individual GA to adjust its own expectations; at the same time, the population of agents are selecting which form of the GA to use. Our results suggest that more exploitative variants of the GA have a greater probability of convergence and a greater probability of convergence to the Pareto superior equilibrium.

The new evolutionary computational paradigm of market systems views these as complex adaptive systems. The major premise of 18 ^th century classical political economy was that order in market systems is spontaneous or emergent, in that it is the result of “human action but not of human design.” This early observation on the disjunction between system wide outcomes and capabilities of micro level rational calculation marks the provenance of modern evolutionary thought. However, it will take a powerful confluence of two 20 ^th century epochal developments for the new evolutionary computational paradigm to rise to the challenge of providing long awaited explanations of what has remained anomalies or outside the ambit of traditional economic analysis. The first of these is the Gödel-Turing-Post results on incompleteness and algorithmically unsolvable problems that delimit formalist calculation or deductive methods. The second is the Anderson-Holland-Arthur heterogeneous adaptive agent theory and models for inductive search, emergence and self-organized criticality which can crucially show and explicitly study the processes underpinning the emergence of ordered complexity. Multi agent model simulation of asset price formation and the innovation based structure changing dynamics of capitalist growth are singled out for analysis of this disjunction between non-anticipating global outcomes and computational micro rationality.