Regular Series

Vol. 37 (2006), No. 11, pp. 2955 – 3192

Electricity Real Options Valuation

Acta Phys. Pol. B 37, 2955 (2006)

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In this paper a real option approach for the valuation of real assets is presented. Two continuous time models used for valuation are described: geometric Brownian motion model and interest rate model. The valuation for electricity spread option under Vasicek interest model is placed and the formulas for parameter estimators are calculated. The theoretical part is confronted with real data from electricity market.

Justice in the Shadow of Self-Interest an Experiment on Redistributive Behavior

Acta Phys. Pol. B 37, 2967 (2006)

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By means of laboratory experiment I examine the relation between fairness judgments made “behind the veil of ignorance” and actual behavior in a model situation of income inequality. As the evidence shows, when material self-interest is at stake vast majority of subjects tend to abandon the fairness norm. Rather small regard for efficiency is present in the data. Furthermore, as low income players go through a sequence of games against high earners and experience changes in income disparity, the history effect proves to override structural characteristics of the redistribution game.

Non-Causal Final Impulse Response Filters for the Maximum Return from Capital Markets

Acta Phys. Pol. B 37, 2979 (2006)

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In this paper we consider a trading strategy, which consists in buying or selling a financial instrument when the smoothing, non-causal FIR (Final Impulse Response) filter output attains a local minimum or maximum, respectively. Upon this assumption the goal of this paper is to determine the “best” non-causal smoothing FIR filters, which provide maximum value of the return from market. The assumed non-causality is obtained by advancing the output signal to compensate for the delay introduced by the a priori known filter. The best results were obtained for the impulse response given by the Pascal triangle and the family of symmetric power triangles, both for the case of trading with, and without the transaction fee. It was found that the transaction fee dramatically reduces a possible net return, and therefore should not be omitted in market analyzes.

Complexity Characteristics of Currency Networks

Acta Phys. Pol. B 37, 2987 (2006)

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A large set of daily FOREX time series is analyzed. The corresponding correlation matrices (CM) are constructed for USD, EUR and PLN used as the base currencies. The triangle rule is interpreted as constraints reducing the number of independent returns. The CM spectrum is computed and compared with the cases of shuffled currencies and a fictitious random currency taken as a base currency. The Minimal Spanning Tree (MST) graphs are calculated and the clustering effects for strong currencies are found. It is shown that for MSTs the node rank has power like, scale free behavior. Finally, the scaling exponents are evaluated and found in the range analogous to those identified recently for various complex networks.

The Asymptotic Dependence of Elliptic Random Variables

Acta Phys. Pol. B 37, 2997 (2006)

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In this paper, we try to answer the question, whether for bivariate elliptic random variable \(X=(X_1,X_2)\) the marginal random variables \(X_1\) and \(X_2\) are asymptotically dependent. We show, that for some special form of the characteristic generator of \(X\) the answer is positive.

On Value at Risk for Foreign Exchange Rates — the Copula Approach

Acta Phys. Pol. B 37, 3005 (2006)

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The aim of this paper is to determine the Value at Risk (\(VaR\)) of the portfolio consisting of long positions in foreign currencies on an emerging market. Basing on empirical data we restrict ourselves to the case when the tail parts of distributions of logarithmic returns of these assets follow the power laws and the lower tail of associated copula \(C\) follows the power law of degree 1. We will illustrate the practical usefulness of this approach by the analysis of the exchange rates of EUR and CHF at the Polish forex market.

Economic and Social Factors in Designing Disease Control Strategies for Epidemics on Networks

Acta Phys. Pol. B 37, 3017 (2006)

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Models for control of epidemics on local, global and small-world networks are considered, with only partial information accessible about the status of individuals and their connections. The main goal of an effective control measure is to stop the epidemic at a lowest possible cost, including treatment and cost necessary to track the disease spread. We show that delay in detection of infectious individuals and presence of long-range links are the most important factors determining the cost. However, the details of long-range links are usually the least-known element of the social interactions due to their occasional character and potentially short life-span. We show that under some conditions on the probability of disease spread, it is advisable to attempt to track those links, even if this involves additional costs. Thus, collecting some additional knowledge about the network structure might be beneficial to ensure a successful and cost-effective control.

Dynamics of the Warsaw Stock Exchange Index as Analysed by the Nonhomogeneous Fractional Relaxation Equation

Acta Phys. Pol. B 37, 3027 (2006)

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We analyse the dynamics of the Warsaw Stock Exchange index WIG at a daily time horizon before and after its well defined local maxima of the cusp-like shape decorated with oscillations. The rising and falling paths of the index peaks can be described by the Mittag–Leffler function superposed with various types of oscillations. The latter is a solution of our model of index dynamics defined by the nonhomogeneous fractional relaxation equation. This solution is a generalised analog of an exactly solvable model of viscoelastic materials. We found that the Warsaw Stock Exchange can be considered as an intermediate system lying between two complex ones, defined by short and long-time limits of the Mittag-Leffler function; these limits are given by the Kohlraush–Williams–Watts law for the initial times, and the power-law or the Nutting law for asymptotic time. Hence follows the corresponding short- and long-time power-law behaviour (different “universality classes”) of the time-derivative of the logarithm of WIG which can in fact be viewed as the “finger print” of a dynamical critical phenomenon.

Asymmetric Matrices in an Analysis of Financial Correlations

Acta Phys. Pol. B 37, 3039 (2006)

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Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and correlation matrices for rich multivariate data. In the latter case one constructs a real symmetric matrix with real non-negative eigenvalues describing the correlation structure of the data. However, if one performs a correlation-function-like analysis of multivariate data, when a stress is put on investigation of delayed dependencies among different types of signals, one can calculate an asymmetric correlation matrix with complex eigenspectrum. From the Random Matrix Theory point of view this kind of matrices is closely related to Ginibre Orthogonal Ensemble (GinOE). We present an example of practical application of such matrices in correlation analyses of empirical data. By introducing the time lag, we are able to identify temporal structure of the inter-market correlations. Our results show that the American and German stock markets evolve almost simultaneously without a significant time lag so that it is hard to find imprints of information transfer between these markets. There is only an extremely subtle indication that the German market advances the American one by a few seconds.

Gossip in Random Networks

Acta Phys. Pol. B 37, 3049 (2006)

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We consider the average probability \(X\) of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erdős and Rényi. In this theory, a network is characterized by two parameters: the size \(N\) and the link probability \(p\). Our experimental data suggest three levels of social inclusion of friendship. The critical value \(p_{\rm c}\), for which half of agents are informed, scales with the system size as \(N^{~-\gamma }\) with \(\gamma \approx 0.68\). Computer simulations show that the probability \(X\) varies with \(p\) as a sigmoidal curve. Influence of the correlations between neighbors is also evaluated: with increasing clustering coefficient \(C\), \(X\) decreases.

Universalism Versus Particularism Through the European Social Survey Lenses

Acta Phys. Pol. B 37, 3059 (2006)

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The cultural variation of economic activity is wide and multidimensional. In my presentation I will refer to the analyses of the culture of capitalism provided by Alfons Trompenaars and Charles Hampden-Turner. According to them there are seven processes and related dilemmas which are important in analyzing the construction of a cultural system of economy. I will focus only on one of them, universalism versus particularism. Using the database of Trompenaars and Hampden-Turner I will show how this dilemma was solved by managers from different European countries. That will be starting point for my analysis of universalism-particularism attitudes of respondents of European Social Survey (ESS). I will be particularly interested in verification of hypothesis on the place of Poland on the mosaic of European cultures of capitalism.

The Dependence Structure for PARMA Models with \(\alpha \)-Stable Innovations

Acta Phys. Pol. B 37, 3071 (2006)

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In this paper we investigate the dependence structure for PARMA models (i.e. ARMA models with periodic coefficients) with symmetric \(\alpha -\)stable innovations. In this case the covariance function is not defined and therefore other measures of dependence have to be used. After obtaining the form of the bounded solution of the PARMA system with symmetric \(\alpha \)-stable innovations, we study the codifference and the covariation — the most popular measures of dependence defined for symmetric stable time series. We show that both considered measures are periodic. Moreover we determine the cases when the codifference and the covariation are asymptotically proportional with the coefficient of proportionality equal to \(\alpha \).

Multifractal Model of Asset Returns Versus Real Stock Market Dynamics

Acta Phys. Pol. B 37, 3083 (2006)

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There is more and more empirical evidence that multifractality constitutes another and perhaps the most significant financial stylized fact. A realistic model of the financial dynamics should therefore incorporate this effect. The most promising in this respect is the Multifractal Model of Asset Returns (MMAR) introduced by Mandelbrot et al. [1] in which multifractality is carried by time deformation. In our study we focus on the Lux extension to MMAR and empirical data from Warsaw Stock Exchange. We show that this model is able to reproduce relevant aspects of the real stock market dynamics.

Bayesian Analysis of the Conditional Correlation Between Stock Index Returns with Multivariate Stochastic Volatility Models

Acta Phys. Pol. B 37, 3093 (2006)

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In the paper we compare the modelling ability of discrete-time multivariate Stochastic Volatility (SV) models to describe the conditional correlations between stock index returns. We consider four tri-variate SV models, which differ in the structure of the conditional covariance matrix. Specifications with zero, constant and time-varying conditional correlations are taken into account. As an example we study tri-variate volatility models for the daily log returns on the WIG, S&P 500, and FTSE 100 indexes. In order to formally compare the relative explanatory power of SV specifications we use the Bayesian principles of comparing statistic models. Our results are based on the Bayes factors and implemented through Markov Chain Monte Carlo techniques. The results indicate that the most adequate specifications are those that allow for time-varying conditional correlations and that have as many latent processes as there are conditional variances and covariances. The empirical results clearly show that the data strongly reject the assumption of constant conditional correlations.

Bayesian Comparison of GARCH Processes with Skewness Mechanism in Conditional Distributions

Acta Phys. Pol. B 37, 3105 (2006)

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The main goal of this paper is an application of Bayesian model comparison, based on the posterior probabilities and posterior odds ratios, in testing the explanatory power of a set of competing GARCH (Generalized Autoregressive Conditionally Heteroscedastic) specifications, all with asymmetric and heavy tailed conditional distributions. In building competing volatility models we consider, as an initial specification, conditionally Student-\(t\) GARCH process with unknown degrees of freedom parameter. By introducing skewness into Student-\(t\) family and incorporating the resulting class as a conditional distribution we generated various GARCH models, which compete in explaining possible asymmetry of both conditional and unconditional distribution of financial data. In order to make Student-\(t\) family skewed we consider various alternative mechanisms recently proposed in the literature. In particular, we apply the hidden truncation mechanism, an approach based on the inverse scale factors in the positive and the negative orthant, order statistics concept, Beta distribution transformation and Bernstein density transformation. Additionally, we consider GARCH process with conditional \(\alpha \)-Stable distribution. Based on the daily returns of hypothetical financial time series, we discuss the results of Bayesian comparison of alternative skewing mechanisms applied in the initial Student-\(t\) GARCH framework. Additionally, we present formal Bayesian inference about conditional asymmetry of the distribution of the daily returns in all competing specifications on the basis of the skewness measure defined by Arnold and Groenveld.

Correlation Matrix Decomposition of WIG20 Intraday Fluctuations

Acta Phys. Pol. B 37, 3123 (2006)

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Using the correlation matrix formalism we study the temporal aspects of the Warsaw Stock Market evolution as represented by the WIG20 index. The high frequency (1 min) WIG20 recordings over the time period between January 2001 and October 2005 are used. The entries of the correlation matrix considered here connect different distinct periods of the stock market dynamics, like days or weeks. Such a methodology allows to decompose the price fluctuations into the orthogonal eigensignals that quantify different modes of the underlying dynamics. The magnitudes of the corresponding eigenvalues reflect the strengths of such modes. One observation made in this paper is that strength of the daily trend in the WIG20 dynamics systematically decreases when going from 2001 to 2005. Another is that large events in the return fluctuations are primarily associated with a few most collective eigensignals.

Penrose Voting System and Optimal Quota

Acta Phys. Pol. B 37, 3133 (2006)

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Systems of indirect voting based on the principle of qualified majority can be analysed using the methods of game theory. In particular, this applies to the voting system in the Council of the European Union, which was recently a subject of a vivid political discussion. The a priori voting power of a voter measures his potential influence over the decisions of the voting body under a given decision rule. We investigate a system based on the law of Penrose, in which each representative in the voting body receives the number of votes (the voting weight) proportional to the square root of the population he or she represents. Here we demonstrate that for a generic distribution of the population there exists an optimal quota for which the voting power of any state is proportional to its weight. The optimal quota is shown to decrease with the number of voting countries.

Automatic Trading Agent. RMT Based Portfolio Theory and Portfolio Selection

Acta Phys. Pol. B 37, 3145 (2006)

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Portfolio theory is a very powerful tool in the modern investment theory. It is helpful in estimating risk of an investor’s portfolio, arosen from lack of information, uncertainty and incomplete knowledge of reality, which forbids a perfect prediction of future price changes. Despite of many advantages this tool is not known and not widely used among investors on Warsaw Stock Exchange. The main reason for abandoning this method is a high level of complexity and immense calculations. The aim of this paper is to introduce an automatic decision-making system, which allows a single investor to use complex methods of Modern Portfolio Theory (MPT). The key tool in MPT is an analysis of an empirical covariance matrix. This matrix, obtained from historical data, biased by such a high amount of statistical uncertainty, that it can be seen as random. By bringing into practice the ideas of Random Matrix Theory (RMT), the noise is removed or significantly reduced, so the future risk and return are better estimated and controlled. These concepts are applied to the Warsaw Stock Exchange Simulator The result of the simulation is 18% level of gains in comparison with respective 10% loss of the Warsaw Stock Exchange main index WIG.

On Capital Dependent Dynamics of Knowledge

Acta Phys. Pol. B 37, 3161 (2006)

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We investigate the dynamics of growth models in terms of dynamical system theory. We analyse some forms of knowledge and its influence on economic growth. We assume that the rate of change of knowledge depends on both the rate of change of physical and human capital. First, we study a model with constant savings. The model with optimised behaviour of households is also considered. We show that the model where the rate of change of knowledge depends only on the rate of change of physical capital can be reduced to the form of the two-dimensional autonomous dynamical system. All possible evolutional paths and the stability of solutions in the phase space are discussed in details. We obtain that the rate of growth of capital, consumption and output are greater in the case of capital dependent rate of change of knowledge.

Efficiency of Pair Formation in a Model Society

Acta Phys. Pol. B 37, 3171 (2006)

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In a recent paper a set of differential equations was proposed to describe a social process, where pairs of partners emerge in a community. The choice was performed on a basis of attractive resources and of random initial preferences. An efficiency of the process, defined as the probability of finding a partner, was found to depend on the community size. Here we demonstrate, that if the resources are not relevant, the efficiency is equal to unity; everybody finds a partner. With this new formulation, about 80 percent of community members enter into dyads; the remaining 20 percent form triads.

The Average Behaviour of Financial Market by 2 Scale Homogenisation

Acta Phys. Pol. B 37, 3177 (2006)

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The financial market is non predictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a market in long terms, such as year intervals, is different from that in short terms. A diffusion equation with a time dependent diffusion coefficient that describes the fluctuations of the financial market, is subject to a two-scale homogenisation, and long term characteristics of the market such as mean behaviour of price and variance, are obtained. We indicate also that introduction of convolution into diffusion equation permits to obtain L-stable behaviour of finance.

Comparison of Gain–Loss Asymmetry Behavior for Stocks and Indexes

Acta Phys. Pol. B 37, 3187 (2006)

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Investment horizon approach has been used to analyze indexes of Polish stock market. Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain–loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and for most stocks of individual companies. The gain–loss asymmetry for these data, measured by a coefficient, that we postulated before [submitted to Physica A], has opposite sign to this for WIG index.


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