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

Updates: Current developments in the discourse field Biodiversity & Climate

With which political developments is BiKF confronted as a research centre as well as concerning its research and transfer efforts? Are there any hints for emerging research questions that meet practical needs? This paper gives an overview – as of June 2010 – on priority issues in the run-up to CBD’s COP-10, the 10th Conference of the Parties to the Convention on Biological Diversity (CBD), which will take place in Nagoya/Japan in October 2010. Highlighted discourse threads are: (1) the state of negotiations for an Access and Benefit Sharing (ABS) regime within CBD, (2) European and international preparations for renewing the political objectives for protecting biodiversity (Post-2010 Targets) and (3) the recent decision on an Intergovernmental Science-Policy Platform for Biodiversity and Ecosystem Services (IPBES). These three threads are selected against the background of an in depth analysis of the discourse field which was carried out in 2008/09 for BiKF. They show how the field progresses and which developments are worth being incorporated into BiKF’s further work. This Knowledge Flow Paper documents the talk given by the author during the second BiKF Retreat, 17–18 July 2010

The Markov-Switching Multifractal Model of asset returns: GMM estimation and linear forecasting of volatility

Multifractal processes have recently been proposed as a new formalism for modelling the time series of returns in insurance. 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 multifractal 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 incurred 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 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

Rational forecasts or social opinion dynamics? Identification of interaction effects in a business climate survey

This paper develops a methodology for estimating the parameters of dynamic opinion or expectation formation processes with social interactions. We study a simple stochastic framework of a collective process of opinion formation by a group of agents who face a binary decision problem. The aggregate dynamics of the individuals' decisions can be analyzed via the stochastic process governing the ensemble average of choices. Numerical approximations to the transient density for this ensemble average allow the evaluation of the likelihood function on the base of discrete observations of the social dynamics. This approach can be used to estimate the parameters of the opinion formation process from aggregate data on its average realization. Our application to a well-known business climate index provides strong indication of social interaction as an important element in respondents' assessment of the business climate. --Business climate,Business cycle forecasts,Opinion formation,Social interactions

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