Dynamics of Markets: The New Financial Economics

Dynamics of Markets provides a careful introduction to stochastic methods along with approximate ensembles for a single, historic time series. This book explains the history leading up to the biggest economic disaster of the 21st century. Empirical evidence for finance market instability under deregulation is given, together with a history of the explosion of the US Dollar worldwide. A model shows how bounds set by a central bank stabilized FX in the gold standard era, illustrating the effect of regulations.

Author’s Note:

This book provides a thorough introduction to econophysics and finance market theory, and leads the reader from the basics to the frontiers of research. These are good times for econophysics with emphasis on market instability, and bad times for the standard economic theory that teaches stable equilibrium of markets. I now explain how the new volume differs in detail from the first edition.

The first edition of Dynamics of Markets (2004) was based largely on our discovery of diffusive dynamics of the exponential model, and more generally on the dynamics of Markovian models with variable diffusion coefficients. Since that time, the progress by the University of Houston Group (Kevin Bassler, Gemunu Gunaratne, and me) has produced a far more advanced market dynamics theory based on our initial discovery. The present book includes our discoveries since 2004.

In particular, we’ve understood the limitations of scaling and one-point densities: given a scaling process, only the one-point density can scale, the transition density and all higher-order densities do not and cannot scale, and a one-point density (as Ha¨ nggi and Thomas pointed out over 30 years ago) cannot be used to identify an underlying stochastic process. Even pair correlations do not scale. It follows that scaling cannot be used to determine the dynamics that generated a time series. In particular, scaling is not an indication of long time correlations, and we exhibit scaling Markov models to illustrate that point. Our focus in this edition is therefore on the pair correlations and transition densities for stochastic processes, representing the minimum level of knowledge required to identify (or rule out) a class of stochastic processes.

The central advances are our 2007 foreign exchange (FX) data analysis, and the Martingale diffusion theory that it indicates. We therefore focus from the start on the pair correlations of stochastic processes needed to understand and characterize a class of stochastic processes. The form of the pair correlations tells us whether we’re dealing with Martingale dynamics, or with the dynamics of long time pair correlations like fractional Brownian motion. The stochastic processes with pair correlations agreeing empirically with detrended finance data are Martingales, and the addition of drift to a Martingale yields an Ito process. We therefore emphasize Ito processes, which are diffusive processes with uncorrelated noise increments. Stated otherwise, the Martingale is the generalization of the Wiener process to processes with general (x,t)-dependent diffusion coefficients. In physics x denotes position; in finance and macroeconomics x denotes the logarithm of a price.

A much more complete development of the theory of diffusive stochastic processes is provided in this text than in the first edition, with simple examples showing how to apply Ito calculus. We show that stationary markets cannot be efficient, and vice versa, and show how money could systematically be made with little or no risk by betting in a stationary market. The Dollar on the gold standard provides the illuminating example.

The efficient market hypothesis is derived as a Martingale condition from the absence of influence of the past on the future at the level of pair correlations. Because of non-stationarity, the analysis of an arbitrary time series is nontrivial. We show how to construct an approximate ensemble for a single historic time series like finance data, and then show how a class of dynamical models can be deduced from the statistical ensemble analysis. Our new FX data analysis is discussed in detail, showing that the dynamics in log returns is a Martingale after a time lag of 10 minutes in intraday trading, and we show how spurious stylized facts are generated by a common but wrong method of data analysis based on time averages.

Contents:

• Econophysics: why and what
• Neo-classical economic theory
• Probability and stochastic processes
• Introduction to financial economics
• Introduction to portfolio selection theory
• Scaling, pair correlations, and conditional densities
• Statistical ensembles: deducing dynamics from time series
• Martingale option pricing
• FX market globalization: evolution of the Dollar to worldwide reserve currency
• Macroeconomics and econometrics: regression models vs empirically based modeling
• Complexity

Dynamics of Markets: The New Financial Economics By Joseph L. McCauley pdf