Marc Potters

Bio: Marc Potters is an academic researcher from Capital Fund Management. The author has contributed to research in topics: Random matrix & Financial market. The author has an hindex of 37, co-authored 97 publications receiving 7658 citations. Previous affiliations of Marc Potters include Weizmann Institute of Science.

Noise Dressing of Financial Correlation Matrices

Abstract: We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series. The central result of the present study, which focuses on the case of financial price fluctuations, is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S 500 (or other major markets). In particular, the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.

Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management

Abstract: Foreword Preface 1. Probability theory: basic notions 2. Maximum and addition of random variables 3. Continuous time limit, Ito calculus and path integrals 4. Analysis of empirical data 5. Financial products and financial markets 6. Statistics of real prices: basic results 7. Non-linear correlations and volatility fluctuations 8. Skewness and price-volatility correlations 9. Cross-correlations 10. Risk measures 11. Extreme correlations and variety 12. Optimal portfolios 13. Futures and options: fundamental concepts 14. Options: hedging and residual risk 15. Options: the role of drift and correlations 16. Options: the Black and Scholes model 17. Options: some more specific problems 18. Options: minimum variance Monte-Carlo 19. The yield curve 20. Simple mechanisms for anomalous price statistics Index of most important symbols Index.

Theory of financial risks : from statistical physics to risk management

Abstract: 1. Probability theory: basic notions 2. Statistics of real prices 3. Extreme risks and optimal portfolios 4. Futures and options: fundamental concepts 5. Options: some more specific problems Glossary.

Random matrix theory and financial correlations

Abstract: We show that results from the theory of random matrices are potentially of great interest when trying to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate financial time series. We find a remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). Finally, we give a specific example to show how this idea can be sucessfully implemented for improving risk management.

Theory of financial risk and derivative pricing

Abstract: Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies

Statistical physics of social dynamics

Abstract: Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Evolution of networks

Abstract: We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrat...

Traffic and related self-driven many-particle systems

Abstract: Since the subject of traffic dynamics has captured the interest of physicists, many surprising effects have been revealed and explained. Some of the questions now understood are the following: Why are vehicles sometimes stopped by ``phantom traffic jams'' even though drivers all like to drive fast? What are the mechanisms behind stop-and-go traffic? Why are there several different kinds of congestion, and how are they related? Why do most traffic jams occur considerably before the road capacity is reached? Can a temporary reduction in the volume of traffic cause a lasting traffic jam? Under which conditions can speed limits speed up traffic? Why do pedestrians moving in opposite directions normally organize into lanes, while similar systems ``freeze by heating''? All of these questions have been answered by applying and extending methods from statistical physics and nonlinear dynamics to self-driven many-particle systems. This article considers the empirical data and then reviews the main approaches to modeling pedestrian and vehicle traffic. These include microscopic (particle-based), mesoscopic (gas-kinetic), and macroscopic (fluid-dynamic) models. Attention is also paid to the formulation of a micro-macro link, to aspects of universality, and to other unifying concepts, such as a general modeling framework for self-driven many-particle systems, including spin systems. While the primary focus is upon vehicle and pedestrian traffic, applications to biological or socio-economic systems such as bacterial colonies, flocks of birds, panics, and stock market dynamics are touched upon as well.

Empirical properties of asset returns: stylized facts and statistical issues

Abstract: We present a set of stylized empirical facts emerging from the statistical analysis of price variations in various types of financial markets. We first discuss some general issues common to all statistical studies of financial time series. Various statistical properties of asset returns are then described: distributional properties, tail properties and extreme fluctuations, pathwise regularity, linear and nonlinear dependence of returns in time and across stocks. Our description emphasizes properties common to a wide variety of markets and instruments. We then show how these statistical properties invalidate many of the common statistical approaches used to study financial data sets and examine some of the statistical problems encountered in each case.

Introduction to Econophysics: Correlations and Complexity in Finance

Abstract: This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.