Artificial intelligence has transformed financial technology in many ways and in this review article, three of the most promising applications are discussed: neural networks, data mining, and pattern recognition. Just as indexes are meant to facilitate the summary and extraction of information in an efficient manner, sophisticated automated algorithms can now perform similar functions but at higher and more powerful levels. In some cases, artificial intelligence can save us from natural stupidity.

We construct a computer simulation of a repeated double-auction market, designed to match those in experimental-market settings with human subjects, to model complex interactions among artificially-intelligent traders endowed with varying degrees of learning capabilities. In the course of six different experimental designs, we investigate a number of features of our agent-based model: the price efficiency of the market, the speed at which prices converge to the rational expectations equilibrium price, the dynamics of the distribution of wealth among the different types of AI-agents, trading volume, bid/ask spreads, and other aspects of market dynamics. We are able to replicate several findings of human-based experimental markets, however, we also find intriguing differences between agent-based and human-based experiments.

This paper examines the stochastic properties of aggregate macroeconomic time series from the standpoint of fractionally integrated models, and focuses on the persistence of economic shocks. We develop a simple macroeconomic model that exhibits long-term dependence, a consequence of aggregation in the presence of real business cycles. We derive the relation between properties of fractionally integrated macroeconomic time series and those of microeconomic data, and discuss how fiscal policy may alter their stochastic behavior. To implement these results empirically, we employ a test for fractionally integrated time series based on the Hurst-Mandelbrot rescaled range. This test is robust to short-term dependence, and is applied to quarterly and annual real GNP to determine the sources and nature of long-term dependence in the business cycle.

The fact that derivative securities are equivalent to specific dynamic trading strategies in complete markets suggests the possibility of constructing buy-and-hold portfolios of options that mimic certain dynamic investment policies, e.g., asset-allocation rules. We explore this possibility by solving the following problem: given an optimal dynamic investment policy, find a set of options at the start of the investment horizon which will come closest to the optimal dynamic investment policy. We solve this problem for several combinations of preferences, return dynamics, and optimality criteria, and show that under certain conditions, a portfolio consisting of just a few options is an excellent substitute for considerably more complex dynamic investment policies.

Given a European derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based, we solve the dynamic replication problem: find a self-financing dynamic portfolio strategy—involving only the underlying securities—that most closely approximates the payoff function at maturity. By applying stochastic dynamic programming to the minimization of a mean-squared-error loss function under Markov state-dynamics, we derive recursive expressions for the optimal-replication strategy that are readily implemented in practice. The approximation error or "epsilon" of the optimal-replication strategy is also given recursively and may be used to quantify the "degree" of market incompleteness. To investigate the practical significance of these epsilon-arbitrage strategies, we consider several numerical examples including path-dependent options and options on assets with stochastic volatility and jumps.

The financial industry is one of the fastest-growing areas of scientific computing. Two decades ago, terms such as financial engineering, computational finance, and financial mathematics did not exist in common usage. Today, these areas are distinct and enormously popular academic disciplines with their own journals, conferences, and professional societies. One explanation for this area’s remarkable growth and the impressive array of mathematicians, computer scientists, physicists, and economists that are drawn to it is the formidable intellectual challenges intrinsic to financial markets. Many of the most basic problems in financial analysis are unsolved and surprisingly resilient to the onslaught of researchers from diverse disciplines. In this article, we hope to give a sense of these challenges by describing a relatively simple problem that all investors face when managing a portfolio of financial securities over time. Such a problem becomes more complex once real-world considerations factor into its formulation. We present the basic dynamic portfolio optimization problem and then consider three aspects of it: taxes, investor preferences, and portfolio constraints. These three issues are by no means exhaustive—they merely illustrate examples of the kinds of challenges financial engineers face today. Examples of other computational issues in portfolio optimization appear elsewhere.

Ever since the publication in 1565 of Girolamo Cardano's treatise on gambling, Liber de Ludo Aleae (The Book of Games of Chance), statistics and financial markets have become inextricably linked. Over the past few decades many of these links have become part of the canon of modern finance, and it is now impossible to fully appreciate the workings of financial markets without them. This selective survey covers three of the most important ideas of finance—efficient markets, the random walk hypothesis, and derivative pricing models—that illustrate the enormous research opportunities that lie at the intersection of finance and statistics.

This book covers the techniques of data mining, knowledge discovery, genetic algorithms, neural networks, bootstrapping, machine learning, and Monte Carlo simulation.

Computational finance, an exciting new cross-disciplinary research area, draws extensively on the tools and techniques of computer science, statistics, information systems, and financial economics. This book covers the techniques of data mining, knowledge discovery, genetic algorithms, neural networks, bootstrapping, machine learning, and Monte Carlo simulation. These methods are applied to a wide range of problems in finance, including risk management, asset allocation, style analysis, dynamic trading and hedging, forecasting, and option pricing. The book is based on the sixth annual international conference Computational Finance 1999, held at New York University's Stern School of Business.

Typical value-at-risk (VAR) calculations involve the probabilities of extreme dollar losses, based on the statistical distributions of market prices. Such quantities do not account for the fact that the same dollar loss can have two very different economic valuations, depending on business conditions. We propose a nonparametric VAR measure that incorporates economic valuation according to the state-price density associated with the underlying price processes. The state-price density yields VAR values that are adjusted for risk aversion, time preferences, and other variations in economic valuation. In the context of a representative agent equilibrium model, we construct an estimator of the risk-aversion coefficient that is implied by the joint observations on option prices and underlying asset value.

The dramatic growth in institutionally managed assets, coupled with the advent of internet trading and electronic brokerage for retail investors, has led to a surge in the size and volume of trading. At the same time, competition in the asset management industry has increased to the point where fractions of a percent in performance can separate the top funds from those in the next tier. In this environment, portfolio managers have begun to explore active management of trading costs as a means of boosting returns. Controlling execution cost can be viewed as a stochastic dynamic optimization problem because trading takes time, stock prices exhibit random fluctuations, and execution prices depend on trade size, order flow, and market conditions. In this paper, we apply stochastic dynamic programming to derive trading strategies that minimize the expected cost of executing a portfolio of securities over a fixed period of time, i.e., we derive the optimal sequence of trades as a function of prices, quantitites, and other market conditions. To illustrate the practical relevance of our methods, we apply them to a hypothetical portfolio of 25 stocks by estimating their price-impact functions using historical trade data from 1996 and deriving the optimal execution strategies. We also perform several Monte Carlo simulation experiments to compare the performance of the optimal strategy to several alternatives.

We examine the implications of portfolio theory for the cross-sectional behavior of equity trading volume. We begin by showing that a two-fund separation theorem suggests a natural definition for trading volume: share turnover. If two-fund separation holds, share turnover must be identical for all securities. If (K+1)-fund separation holds, we show that share turnover satisfies and approximate linear K-factor structure, These implications are empirically tested using weekly turnover data for NYSE and AMEX securities from 1962 to 1996. We find strong evidence against two-fund separation and an eigenvalue decomposition suggests that volume is driven by a two-factor linear model. Click here to download Trading Volume and the MiniCRSP Database: An Introduction and User’s Guide for instructions on how to create your own MiniCRSP database.

In this paper we study the tracking error resulting from the discrete-time application of continuous-time delta-hedging procedures for European options. We characterize the asymptotic distribution of the tracking error as the number of discrete time periods increases, and its joint distribution with other assets. We introduce the notion of temporal granularity of the continuous-time stochastic model that enables us to characterize the degree to which discrete-time approximations of continuous time models track the payoff of the option. We derive closed form expressions for the granularity for a put and call option on a stock that follows a geometric Brownian motion and a mean-reverting process. These expressions offer insight into the tracking error involved in applying continuous-time delta-hedging in discrete time. We also introduce alternative measures of the tracking error and analyze their properties.

Technical analysis, also known as "charting,'' has been a part of financial practice for many decades, but this discipline has not received the same level of academic scrutiny and acceptance as more traditional approaches such as fundamental analysis. One of the main obstacles is the highly subjective nature of technical analysis—the presence of geometric shapes in historical price charts is often in the eyes of the beholder. In this paper, we propose a systematic and automatic approach to technical pattern recognition using nonparametric kernel regression, and apply this method to a large number of U.S. stocks from 1962 to 1996 to evaluate the effectiveness of technical analysis. By comparing the unconditional empirical distribution of daily stock returns to the conditional distribution—conditioned on specific technical indicators such as head-and-shoulders or double-bottoms—we find that over the 31-year sample period, several technical indicators do provide incremental information and may have some practical value.

For over half a century, financial experts have regarded the movements of markets as a random walk--unpredictable meanderings akin to a drunkard's unsteady gait--and this hypothesis has become a cornerstone of modern financial economics and many investment strategies. Here Andrew W. Lo and A. Craig MacKinlay put the Random Walk Hypothesis to the test. In this volume, which elegantly integrates their most important articles, Lo and MacKinlay find that markets are not completely random after all, and that predictable components do exist in recent stock and bond returns. Their book provides a state-of-the-art account of the techniques for detecting predictabilities and evaluating their statistical and economic significance, and offers a tantalizing glimpse into the financial technologies of the future.

Current risk-management practices are based on probabilities of extreme dollar losses (e.g., measures like Value at Risk), but these measures capture only part of the story. Any complete risk-management system must address two other important factors: prices and preferences. Together with probabilities, these comprise the three P's of Total Risk Management. This article describes how the three Ps interact to determine sensible risk profiles for corporations and for individuals, guidelines for how much risk to bear and how much to hedge. By synthesizing existing research in economics, psychology, and decision sciences, and through an ambitious research agenda to extend this synthesis into other disciplines, a complete and systematic approach to rational decision-making in an uncertain world is within reach.