Fully electronic market will be ubiquitous in the near future. Because financial markets are the most efficient and best studied of all markets, they can provide unique insights in designing the next generation of electronic markets. In particular, in addition to automated electronic financial markets, there will be similar markets for bandwidth, for telephone time, and for many other commodities. The electronic markets of the future will achieve real-time, efficient and transparent allocation of resources between people and organizations and within electronic networks. In this project, we propose to study computational systems of loosely coupled, asynchronous, adaptable software agents with learning abilities. We will design, implement, and characterize artificial markets in which software agents endowed with different learning modules can interact, evolve, and compete.
The tremendous growth in equity trading over the past 20 years, fueled largely by the burgeoning assets of institutional investors such as mutual and pension funds, has created a renewed interest in the measurement and management of trading costs. Such costs - often called "execution costs" because they are associated with the execution of investment strategies - include commissions, bid/ask spreads, opportunity costs of waiting, and price impact from trading, and they can have a substantial impact on investment performance. This "implementation shortfall" is surprisingly large and underscores the importance of execution-cost control, particularly for institutional investors whose trades often comprise a large fraction of the average daily volume of many stocks. there has also been considerable interest from the regulatory perspective in defining "best" execution, especially in the wake of recent concerns about NASDAQ trading practices, the impact of tick size on trading costs, and the economic consequences of market fragmentation. In this project, we propose to explore the impact of transaction costs on optimal portfolio selection and trading behavior in two ways: (1) deriving best-execution trading strategies under specific functional forms for price dynamics and price-reaction functions; and (2) deriving the general equilibrium implications of transactions costs for asset prices and trading volume.
Lo, a., Mamaysky H. and J. Wang, 2001, "Asset Prices and Trading Volume under Fixed Transaction Costs," LFE Working Paper No. LFE-1042-02.
Lo, A. and J. Wang, 2000, "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," Review of Financial Studies 13, 257-300.
Lo, A., MacKinlay, C. and J. Zhang, 2002, "Econometric Models of Limit-Order Executions'', Journal of Financial Economics 65, 31-71.
Bertsimas, D., Hummel, P. and A. Lo, 1999, "Optimal Control of Execution Costs for Portfolios,'' Computing in Science & Engineering, 1, 40-53.
Bertsimas, D. and A. Lo, 1998, "Optimal Control of Execution Costs'', Journal of Financial Markets 1, 1-50.
Delta-hedging strategies play central role in the theory of derivatives and in our understanding of dynamic notions of spanning and market completeness. In particular, delta-hedging strategies are recipes for replicating the payoff of a complex security by sophisticated dynamic trading of simpler securities. When markets are dynamically complete and continuous trading is feasible, it is possible to replicate certain derivative securities perfectly. However, when markets are not complete or when continuous trading is not feasible, e.g., trading frictions or periodic market closings, perfect replication is not possible. In this project, we propose to study the optimal replication problem: given a European derivative security with an arbitrary payoff function and a corresponding set of underlying securities on which the derivative security is based, find a self-financing dynamic portfolio strategy - involving only the underlying securities - that most closely approximates the payoff function at maturity. The fact that derivative securities are equivalent to specific dynamic trading strategies in complete markets suggests another possibility: 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 related optimal-replication problem: given an optimal dynamic investment policy, find a set of options at the start of the investment horizon that will come closest to the optimal dynamic investment policy.
Haugh, M. and A. Lo, 2001, "Asset Allocation and Derivartives," Quantitative Finance 1, 45-72.
Bertsimas, D., Lo, A., and L. Kogan, 2001, "Hedging Derivative Securities and Incomplete Markets: An ε-Arbitrage Approach'', Operations Research 49, 372-397.
Bertsimas, D., Lo, A., and L. Kogan, 2000, "When Is Time Continuous?'', Journal of Financial Economics, 55, 173-204.
Lo, A. and J. Wang, 1995, "Implementing Option Pricing Models When Asset Returns Are Predictable'', Journal of Finance 50, 87--129.
Hutchinson, J., Lo, A., and T. Poggio, 1994, "A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks'', Journal of Finance 49, 851--889.
Our aim is to illustrate the wide application of option pricing theory. We have collected, categorized and indexed a list of over 1400 research articles since 1980 that have cited the option-pricing research of Fischer Black, Robert Merton, and Myron Scholes. At this web site, you may
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Robert Merton, Petr Adamek, Li Jin, Leonid Kogan,Terence Lim, Andrew Lo, Jonathan Taylor, Terence Lim
In this project, we hope to expand our understanding of trading volume by developing well-articulated economic models of asset prices and volume and empirically estimating them using recently available daily volume data for individual securities from the University of Chicago's Center for Research in Securities Prices (CRSP) from 1962 to 1996.
In Phase I we plan to derive the volume implications of classical static portfolio theory, i.e., mutual-fund separation theorems. We then use these implications to define appropriate measures of trading activity for individual securities and for portfolios. Once the definition of volume has been settled, we shall provide extensive descriptive statistics and data analysis that capture the historical behavior of the weekly volume/returns database extract that we have constructed from the CRSP Daily Master File. We then test the implications of mutual-fund separation theorems by examining the empirical properties of the cross section of volume. Given the far-reaching impact of mutual-fund separation theorems, e.g., the CAPM and APT, exploring their volume implications is particularly important because it provides new testable implications to these well-worn paradigms. In much the same way that asset-market models such as the CAPM have guided empirical investigations of the time-series and cross-sectional properties of asset returns, we show that the volume implications of these models provide similar guidelines for investigating the behavior of trading activity.
In Phase II we plan to develop and estimate the volume implications of dynamic equilibrium models of asset markets such as the Intertemporal Capital Asset Pricing Model (ICAPM). These implications include price/volume relations, volatility/volume relations, and the interaction between the time-series and cross-sectional properties of volume and returns. To the extent that both prices and trading are driven by changes in economic conditions, volume, in addition to prices, contains important information about such conditions. Popular asset-market models make specific predictions about how volume is related to changes in underlying economic variables. Testing these predictions allows us to establish the relation between volume and these economic variables. Using the volume data to identify these variables, we can better understand how these variables are driving asset prices.
In Phase III we will investigate the implications of heuristic investment strategies such as "technical" trading rules and other behavioral models of trading activity. While such rules are more difficult to rationalize within the standard economic paradigm, nevertheless they do provide some insight into the more practical aspects of trading activity. We plan to investigate these heuristics in several ways: theoretically (by developing more formal economic models that are consistent with these heuristics), empirically (by estimating the performance of these heuristics using historical data), and experimentally (by conducting controlled trading exercises in the MIT Sloan School's Trading Laboratory).
In Phase IV we will develop the necessary infrastructure to provide internet access to our volume/returns database extract of the CRSP data to all current subscribers of CRSP. This includes user-guide documentation, database construction sourcecode, and sample empirical analyses to facilitate research in this area. If resources permit, we also hope to establish a website for volume researchers which will archive research papers in this area and maintain various non-proprietary volume databases.
Lo, A. and J. Wang, 2001, "The Econometrics of Trading Volume," to appear in Handbook of Financial Econometrics, Amsterdam: North-Holland.
Lo, A. and J. Wang, 2001, "Trading Volume," to appear in Advances in Economic Theory: Eight World Congress (Econometric Society Monograph).
Lo, A. and J. Wang, 2000, "Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory," Review of Financial Studies, 13, 257-300.
Lo, A. and J. Wang, 2001, "Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model," LFE Working Paper No. LFE-1037-01.
Adamek, P., Lim, T., Lo, A. and J. Wang, 1998, "Trading Volume and the MiniCRSP Database: An Introduction and User's Guide'',LFE Working Paper No. LFE-1038-98.
Over the last decade, financial markets have channeled trillions of dollars in investments to the real estate and lending markets. Structured finance facilitated this process by re-engineering loans and receivables into securities offering new profiles of risk and return to investors. In this project, we will combine structured finance and portfolio theory to design a new family of mega social funds. These funds will offer investors a set of attractive securities with unique risk return profiles while multiplying the resources available for scientific research. The main objectives of the project are:
Our ultimate goals are to offer a realistic solution to this challenge, to design a new mechanism to raise new pools of funds for science, and to prove that structured finance can play a role in finding answers to some of the problems facing human kind.