Chia-Hsuan Yeh

On the emergent properties of artificial stock markets: the efficient market hypothesis and the rational expectations hypothesis

Abstract By studying two well known hypotheses in economics, this paper illustrates how emergent properties can be shown in an agent-based artificial stock market. The two hypotheses considered are the efficient market hypothesis and the rational expectations hypothesis. We inquire whether the macrobehavior depicted by these two hypotheses is consistent with our understanding of the microbehavior. In this agent-based model, genetic programming is applied to evolving a population of traders learning over time. We first apply a series of econometric tests to show that the EMH and the REH can be satisfied with some portions of the artificial time series. Then, by analyzing traders’ behavior, we show that these aggregate results cannot be interpreted as a simple scaling-up of individual behavior. A conjecture based on sunspot-like signals is proposed to explain why macrobehavior can be very different from microbehavior. We assert that the huge search space attributable to genetic programming can induce sunspot-like signals, and we use simulated evolved complexity of forecasting rules and Granger causality tests to examine this assertion.

Toward a computable approach to the efficient market hypothesis: An application of genetic programming

Abstract From a computation-theoretic standpoint, this paper formalizes the notion of unpredictability in the efficient market hypothesis (EMH) by a biological-based search program, i.e., genetic programming (GP). This formalization differs from the traditional notion based on probabilistic independence in its treatment of search. Compared with the traditional notion, a GP-based search provides an explicit and efficient search program upon which an objective measure for predictability can be formalized in terms of search intensity and chance of success in the search. This will be illustrated by an example of applying GP to predict chaotic time series. Then the EMH based on this notion will be exemplified by an application to the Taiwan and US stock market. A short-term sample of TAIEX and S&P 500 with the highest complexity defined by Rissanens minimum description length principle (MDLP) is chosen and tested. It is found that, while linear models cannot predict better than the random walk, a GP-based search can beat random walk by 50%. It, therefore, confirms the belief that while the short-term nonlinear regularities might still exist, the search costs of discovering them might be too high to make the exploitation of these regularities profitable, hence the efficient market hypothesis is sustained.

Hedging Derivative Securities with Genetic Programming

One of the most recent applications of GP to finance is to use genetic programming to derive option pricing formulas. Earlier studies take the Black–Scholes model as the true model and use the artificial data generated by it to train and to test GP. The aim of this paper is to provide some initial evidence of the empirical relevance of GP to option pricing. By using the real data from S&P 500 index options, we train and test our GP by distinguishing the case in-the-money from the case out-of-the-money. Unlike most empirical studies, we do not evaluate the performance of GP in terms of its pricing accuracy. Instead, the derived GP tree is compared with the Black–Scholes model in its capability to hedge. To do so, a notion of tracking error is taken as the performance measure. Based on the post-sample performance, it is found that in approximately 20% of the 97 test paths GP has a lower tracking error than the Black–Scholes formula. We further compare our result with the ones obtained by radial basis functions and multilayer perceptrons and one-stage GP. Copyright  1999 John Wiley & Sons, Ltd.

Modeling Speculators with Genetic Programming

In spirit of the earlier works done by Arthur (1992) and Palmer et al. (1993), this paper models speculators with genetic programming (GP) in a production economy (Muthian Economy). Through genetic programming, we approximate the consequences of “speculating about the speculations of others”, including the price volatility and the resulting welfare loss. Some of the patterns observed in our simulations are consistent with findings in experimental markets with human subjects. For example, we show that GP-based speculators can be noisy by nature. However, when appropriate financial regulations are imposed, GP-based speculators can also be more informative than noisy.

Equilibrium Selection via Adaptation: Using Genetic Programming to Model Learning in a Coordination Game

This paper models adaptive learning behavior in a simple coordination game that Van Huyck, Cook and Battalio (1994) have investigated in a controlled laboratory setting with human subjects. We consider how populations of arti- ficially intelligent players behave when playing the same game. We use the genetic programming paradigm, as developed by Koza (1992, 1994), to model how a population of players might learn over time. In genetic programming one seeks to breed and evolve highly fit computer programs that are capable of solving a given problem. In our application, each computer program in the population can be viewed as an individual agent’s forecast rule. The various forecast rules (programs) then repeatedly take part in the coordination game evolving and adapting over time according to principles of natural selection and population genetics.We argue that the genetic programming paradigm that we use has certain advantages over other models of adaptive learning behavior in the context of the coordination game that we consider. We find that the pattern of behavior generated by our population of artificially intelligent players is remarkably similar to that followed by the human subjects who played the same game. In particular, we find that a steady state that is theoretically unstable under a myopic, best-response learning dynamic turns out to be stable under our genetic-programming-based learning system, in accordance with Van Huyck et al.’s (1994) finding using human subjects. We conclude that genetic programming techniques may serve as a plausible mechanism for modeling human behavior, and may also serve as a useful selection criterion in environments with multiple equilibria.

Modeling the expectations of inflation in the OLG model with genetic programming

Abstract In this paper, genetic programming (GP) is employed to model learning and adaptation in the overlapping generations model, one of the most popular dynamic economic models. Using a model of inflation with multiple equilibria as an illustrative example, we show that our GP-based agents are able to coordinate their actions to achieve the Pareto-superior equilibrium (the low-inflation steady state) rather than the Pareto inferior equilibrium (the high-inflation steady state). We also test the robustness of this result with different initial conditions, economic parameters, GP control parameters, and the selection mechanism. We find that as long as the survival-of-the-fittest principle is maintained, the evolutionary operators are only secondarily important. However, once the survival-of-the-fittest principle is absent, the well-coordinated economy is also gone and the inflation rate can jump quite wildly. To some extent, these results shed light on the biological foundations of economics.

Genetic Programming, Predictability and Stock Market Efficiency

Abstract From a computation-theoretic standpoint, this paper formalizes the notion of unpredictability in the efficient market hypothesis (EMH) by a biological-based search program, i.e., genetic programming (GP). This formalization differs from the traditional notion based on probabilistic independence in its treatment of search. While search plays an important role in the EMH, tradtional notion does not formalize serach in a way such that it can be implemented, and it turns out that the EMH based on this notion is practically uncomputable. Compared with the traditional notion, a GP-based search provided an explicit and efficient search program upon which an objective measure for predictability can be formalized in terms of search intensity and chance of success in the search. This will be illustrated by an example of applying GP to predict chaotic time series. Then, the EMH based on this notion will be exemplified by an application to the Taiwan stock market. A short-term sample with the highest complexity defined by Rissanen’s MDLP (Minimum Description Length Principle) is chosen and tested. It is found that, while linear models cannot predict better than the random walk, a GP-based search can beat random walk by 50%. It therefore confirms the belief that short-term nonlinear regularities might still exist despite the fact that in the long-run the market is still remarkably efficient.

Bridging the gap between nonlinearity tests and the efficient market hypothesis by genetic programming

Applies the genetic programming (GP) based notion of unpredictability to the testing of the efficient market hypothesis (EMH). This paper extends the study of Chen and Yeh (1995) by testing the EMH with a small, medium and large sample of the S&P 500 stock index. It is found that, in terms of the prediction performance, the probability /spl pi//sub 2/(n) that GP can beat the random walk tends to have a negative relation to the size of the in-sample dataset. For example, when the sample size n is 50, 200 and 2000, then /spl pi//sub 2/(n) is 0.5, 0.2 and 0, respectively. This therefore suggests that, while nonlinear regularities could exist, they might exist in a very short span. As a consequence, the search costs of discovering them might be too high to make the exploitation of these regularities profitable; hence, the EMH is sustained.

Genetic Programming in the Overlapping Generations Model: An Illustration with the Dynamics of the Inflation Rate

In this paper, genetic programming (GP) is employed to model learning and adaptation in the overlapping generations model, one of the most popular dynamic economic models. Using a model of inflation with multiple equilibria as an illustrative example, we show that our GP-based agents are able to coordinate their actions to achieve the Pareto-superior equilibrium (the low-inflation steady state) rather than the Pareto-inferior equilibrium (the high-inflation steady state). We also test the robustness of this result with different initial conditions, economic parameters, and GP control parameters.