New Mathematics and Natural Computation

This paper presents a basic theory of intelligent finance as a new paradigm of financial investment. It is assumed that the financial market is always in a state of swing between efficient and inefficient modes on multiple levels of time scale; it is possible to go beyond the efficient market theory to study the dynamic evolving process of the market between equilibrium and far-from-equilibrium; there are robust dynamic patterns in this evolving process, which may be exploitable via intelligent trading systems. On the foundation of the four principles — comprehensive, predictive, dynamic and strategic, the basic theory takes the information sources into the loop as the starting points for all the market analysis, introducing the scale space of time into the pricing process analysis in order to detect and capture trends, cycles and seasonality on multiple intrinsic levels of time scale which are then used as the dynamic basis for constructing and managing portfolios. In stock markets, the theory exhibits itself in the form of an Intelligent Dynamic Portfolio Theory, which integrates predictive modeling of a bull-bear market cycle, sector rotation, and portfolio optimization with a reactive trend following trading strategy.

Determining the circumstances under which it is possible to make any sort of prediction is a fundamental question in financial research. The presence of complex and robust statistical characteristics, exhibited by most financial time series, raise doubts on the simple relationship between information and price changes, as implied by the efficient market hypothesis. In this paper, we consider the main competing economic hypotheses and examine different approaches for learning the price behaviour in financial markets. Our analysis reveals the need to approach the problem from a new perspective. In financial markets, traders are not only adapting, but also determine and form the economic mechanism essentially by their actions. In these settings, financial markets are evolutionary structures of competing trading strategies; prices in such markets are driven endogenously by the induced expectations. A combination of economics, computer and cognitive science in cross-disciplinary study of intelligent finance, which aims to explore information about financial markets from multiple perspectives, is expected to expand the boundary of pure economic analysis.

In the first part of this review, we survey the known analytic results regarding the non-ergodic phase of standard Minority Games. Such phases are characterized by the fact that, at odds with ergodic regimes, the steady state properties of the game (e.g. the volatility) depend both on the initial conditions chosen for the agents' learning process as well as on the learning rate. Secondly, we present a discussion of the effects of finite-memory learning, which lifts the non-ergodicity, in the context of spherical Minority Games.

This paper investigates the predictability of moving average rules for the China stock market. We find that buy signals generate higher returns and less volatility, while returns following sell signals are negative and more volatile. Moreover, the bootstrapping results indicate that the asymmetrical patterns of return and volatility between buy and sell signals cannot be explained by four popular linear models of returns, especially the phenomenon of negative sell returns. We then test the nonlinear dynamic process of returns. Although the existing artificial neural network (ANN) model can replicate the negative sell returns, it fails to capture the volatility patterns of buy and sell returns. Furthermore, we introduce the conditional heteroskedasticity structure into the ANN model and find that the revised ANN model cannot only explain the predictability of returns, but can also capture the patterns of buy and sell volatility, which are never achieved by any linear model of returns tested in the related literature. Therefore, we conclude that the moving average trading rules can pick up some of the hidden nonlinear patterns in the dynamic process of stock returns, which may be the reason why they can be used to predict price changes.

In this study, a novel forecasting model based on the Wavelet Neural Network (WNN) is proposed to predict the monthly crude oil spot price. In the proposed model, the OECD industrial petroleum inventory level is used as an independent variable, and the Wavelet Neural Network (WNN) is used to explore the nonlinear relationship between inventories and the price. For verification purposes, the West Texas Intermediate (WTI) crude oil spot price is used for the tested target. Experimental results reveal that the WNN can model the nonlinear relationship between inventories and the price very well. Furthermore, the in-sample and out-of-sample prediction performance also demonstrates that the WNN-based forecasting model can produce more accurate prediction results than other nonlinear and linear models, even when the lengths of the forecast horizon are relatively short or long.

In this paper, a hybrid model integrating wavelet decomposition and least squares support machines (LSSVM) is proposed for crude oil price forecasting. In this model, the Haar à trous wavelet transform is first selected to decompose an original time series into several sub-series with different scales. Then the LSSVM is used to predict each sub-series. Subsequently, the final oil price forecast is obtained by reconstructing the results of the sub-series forecasts. The experimental results show that the integrated model, based on multi-scale wavelet decomposition, outperforms the traditional single-scale models. Furthermore, the proposed hybrid model is the best among all the models compared in this study. To fully integrate the advantages of several models, a combined forecasting model is presented. The study shows that the combined forecasting model is clearly better than any individual model for crude oil price forecasting.

In this paper, a comprehensive review of the valuation of American options is presented. Various approaches to pricing American option contracts are discussed, with the pros and cons of each being briefly outlined. The paper aims to provide a literature review for those who are interested in this very fundamental research, that provides a basis for pricing any American-style derivatives.

This paper examines the price performance of call warrants in China's securities market. A recent sample of daily call warrant prices observed during the period from August 2005 to March 2007 is used. To the best of our knowledge this is the only recent study to using data from China and as such it greatly enhances our understanding of this particular market. On average, we find that the observed market prices are irrationally higher than the Black-Scholes model prices by 80.38% (using 180-day historical volatility) and 140.50% (using EGARCH volatility). However, we find another anomalous phenomenon that some of the call warrants prices are not only lower than the model prices, but have also recently been anomalously under their lower bounds. This finding seems to violate the "no arbitrage" principle. Among the convincing reasons, our findings indicate that trading mechanism constraints in China's securities market prevent rational investors from driving the prices of these call warrants to a reasonable level. Arbitrage chances are found to exist in some specific cases when the call warrant prices are below their lower bounds.

The purpose of this study is to address the inference problem of the parameters of autoregressive conditional heteroscedasticity (ARCH) models. Specifically, we present a comparison of the two approaches — Bayesian and Maximum Likelihood (ML) for ARCH models, and the specific mathematical and algorithmic formulations of these approaches. In the ML, estimation we obtain confidence intervals by using the Bootstrap simulation technique. In the Bayesian estimation, we present a reparametrization of the model which allows us to apply prior normal densities to the transformed parameters. The posterior estimates are obtained using Monte Carlo Markov Chain (MCMC) methods. The methodology is exemplified by considering two Brazilian financial time series: the Bovespa Stock Index — IBovespa and the Telebrás series. The order of each ARCH model is selected by using the Bayesian Information Criterion (BIC).