A prognosis oriented microscopic stock market model

We present a new microscopic stochastic model for an ensemble of interacting investors that buy and sell stocks in discrete time steps via limit orders based on individual forecasts about the price of the stock. These orders determine the supply and demand fixing after each round (time step) the new price of the stock according to which the limited buy and sell orders are then executed and new forecasts are made. We show via numerical simulation of this model that the distribution of price differences obeys an exponentially truncated Levy-distribution with a self similarity exponent mu~5.Comment: 14 pages RevTeX, 5 eps-figures include

The Markov-switching multi-fractal model of asset returns: GMM estimation and linear forecasting of volatility

Multi-fractal processes have recently been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found in virtually all financial data. Initial difficulties stemming from non-stationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multi-fractal model in Calvet and Fisher (2001) which allows for estimation of its parameters via maximum likelihood and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative GMM estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular Binomial and Lognormal models and that the loss incured with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series. --Markov-switching,Multifractal,Forecasting,Volatility,GMM estimation

The multi-fractal model of asset returns : its estimation via GMM and its use for volatility forecasting

Multi-fractal processes have been proposed as a new formalism for modeling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found to characterize virtually all financial prices. Furthermore, elementary variants of multi-fractal models are very parsimonious formalizations as they are essentially one-parameter families of stochastic processes. The aim of this paper is to provide the characteristics of a causal multi-fractal model (replacing the earlier combinatorial approaches discussed in the literature), to estimate the parameters of this model and to use these estimates in forecasting financial volatility. We use the auto-covariances of log increments of the multi-fractal process in order to estimate its parameters consistently via GMM (Generalized Method of Moment). Simulations show that this approach leads to essentially unbiased estimates, which also have much smaller root mean squared errors than those obtained from the traditional ?scaling? approach. Our empirical estimates are used in out-of-sample forecasting of volatility for a number of important financial assets. Comparing the multi-fractal forecasts with those derived from GARCH and FIGARCH models yields results in favor of the new model: multi-fractal forecasts dominate all other forecasts in one out of four cases considered, while in the remaining cases they are head to head with one or more of their competitors. --multi-fractality , financial volatility , forecasting

Quench dynamics and statistics of measurements for a line of quantum spins in two dimensions

Motivated by recent experiments, we investigate the dynamics of a line of spin-down spins embedded in the ferromagnetic spin-up ground state of a two-dimensional xxz model close to the Ising limit. In a situation where the couplings in x and y direction are different, the quench dynamics of this system is governed by the interplay of one-dimensional excitations (kinks and holes) moving along the line and single-spin excitations evaporating into the two-dimensional background. A semiclassical approximation can be used to calculate the dynamics of this complex quantum system. Recently, it became possible to perform projective quantum measurements on such spin systems, allowing to determine, e.g., the z-component of each individual spin. We predict the statistical properties of such measurements which contain much more information than correlation functions.Comment: 10 pages, 7 figure

Detecting multi-fractal properties in asset returns : the failure of the scaling estimator

It has become popular recently to apply the multifractal formalism of statistical physics (scaling analysis of structure functions and f(a) singularity spectrum analysis) to financial data. The outcome of such studies is a nonlinear shape of the structure function and a nontrivial behavior of the spectrum. Eventually, this literature has moved from basic data analysis to estimation of particular variants of multi-fractal models for asset returns via fitting of the empirical t(q) and f(a) functions. Here, we reinvestigate earlier claims of multi-fractality using four long time series of important financial markets. Taking the recently proposed multi-fractal models of asset returns as our starting point, we show that the typical ?scaling estimators? used in the physics literature are unable to distinguish between spurious and ?real? multi-scaling of financial data. Designing explicit tests for multi-scaling, we can in no case reject the null hypothesis that the apparent curvature of both the scaling function and the Hölder spectrum are spuriously generated by the particular fattailed distribution of innovations characterizing financial data. Given the well-known overwhelming evidence in favor of different degrees of long-term dependence in the powers of returns, we interpret this inability to reject the null hypothesis of multi-scaling as a lack of discriminatory power of the standard approach rather than as a true rejection of multi-scaling in financial data. However, the complete ?failure? of the multi-fractal apparatus in this setting also raises the question whether results in other areas (like geophysics) suffer from similar short-comings of the traditional methodology. --

Financial power laws: Empirical evidence, models, and mechanism

Financial markets (share markets, foreign exchange markets and others) are all characterized by a number of universal power laws. The most prominent example is the ubiquitous finding of a robust, approximately cubic power law characterizing the distribution of large returns. A similarly robust feature is long-range dependence in volatility (i.e., hyperbolic decline of its autocorrelation function). The recent literature adds temporal scaling of trading volume and multi-scaling of higher moments of returns. Increasing awareness of these properties has recently spurred attempts at theoretical explanations of the emergence of these key characteristics form the market process. In principle, different types of dynamic processes could be responsible for these power-laws. Examples to be found in the economics literature include multiplicative stochastic processes as well as dynamic processes with multiple equilibria. Though both types of dynamics are characterized by intermittent behavior which occasionally generates large bursts of activity, they can be based on fundamentally different perceptions of the trading process. The present chapter reviews both the analytical background of the power laws emerging from the above data generating mechanism as well as pertinent models proposed in the economics literature. --

Keeping America Fed and Healthy During World War II: Sylvia Brooklyn Denhoff, Home Economist

World War II served as a major force for change in the lives of many American women. Whether on the home front or overseas, the wives, mothers, sisters, and daughters of the United States played an integral role in the American quest for victory. One such woman was Sylvia Brooklyn Denhoff. With a degree in home economics from Syracuse University, Sylvia was hired in 1943 to write “food columns” for the left-wing newspaper PM. Her columns contained information on substitutes for scarce foods, such as meat and butter, the importance of observing price ceilings, recipes for healthy, nutritious meals, and the point system of rationing. Drawing from the more than 150 “food columns” that she wrote as well as extensive interviews with the author, this paper provides an in-depth analysis of Sylvia’s work at PM . It illustrates how her advice on how to make-do during the trying days of rationing and food shortages was a crucial part of the United States government’s mission to get American women on the home front to do their part for the war effort by conserving food, abiding by rationing restrictions, and ensuring that that their families ate nutritious meals