Acta Oeconomica Pragensia, 2005 (vol. 13), issue 1
Local Stability and Bifurcations in Kaldor Model
Roman Binter, Lukáš Vácha
Acta Oeconomica Pragensia 2005, 13(1):10-20 | DOI: 10.18267/j.aop.123 
We analyze a discrete version of a simple Kaldor model. As is typical for Kaldor model we consider an S shaped investment function. This leads to either a one or three equilibria of the model. For simplicity reasons we do not consider an S shape saving function as assumed in the original Kaldor paper. This does not affect any analytical conclusions as for presentation of dynamic properties nonlinear investment function is sufficient. Our aim is to study changes in the model dynamics under varying parameters. We study transition between one and two equilibria setup and also each of the set up separately.
Choice between the Discrete and Continuous Models in Economic Applications and Its Implications
Petr Kadeřábek
Acta Oeconomica Pragensia 2005, 13(1):18-25 | DOI: 10.18267/j.aop.124
When building a dynamic model we express an impact of past on future state variables. We usually know if the change should be positive or negative and have an idea about a magnitude of the change. But if we express the change with either a difference or a derivative often depends on such factors, as is ease of evaluation of discrete models. We show that this choice may have important stability implications. We choose a more general approach and consider the choice not only between discrete and continuous models but among discrete models with various lengths of the step (considering a continuous model be a discrete model with infinitely small step)....
A Small-Open-Economy Model and Endogenous Money Stock
Jan Kodera, Miloslav Vošvrda, Karel Sladký
Acta Oeconomica Pragensia 2005, 13(1):26-35 | DOI: 10.18267/j.aop.125
The purpose of this paper is to study a three-equation dynamic model. The first equation describes the commodity market. The second one demonstrates the dynamics of the money market and the third equation is the interest rate parity. The aim is to investigate the conditions of more complex behaviour of the model. The more complex dynamic behaviour, i.e., limit cycles, could appear when nonlinear investment function is used in the model, for example. Furthermore the nonlinear function of money supply depending on interest rate is used in the model.
Risk Quantification - Early History of Option Pricing
Jaroslav Brada
Acta Oeconomica Pragensia 2005, 13(1):36-40 | DOI: 10.18267/j.aop.128
The article reminds of the world of futures contracts closed between subjects in the Austrian-Hungarian economic space in the period of ca. 1986-1914; an approach to the pricing of option contracts more than 100 years ago is elucidated. The form of a phenomenon of that time that will be called call-put parity in the future is explained. The author describes the procedure of option contract pricing in the form as it was known to our ancestors; this is the reason why he does not use mathematically formalised notation that was developed later.
Performance of Selected Models with Heterogeneous Expectation Formation
Dita Fuchsová
Acta Oeconomica Pragensia 2005, 13(1):41-45 | DOI: 10.18267/j.aop.129
The Efficient Market Hypothesis (EMH) asserts that the prices of securities correctly and fully reflect all available information. But there are some empirical facts in capital markets thatEMHis not able to explain. Recently, a lot of new models with heterogeneous agents in expectation formation of future asset prices have arisen. The main aim of this paper is to compare three of them - model introduced by C. Chiarella in 1992, where the equilibrium price is determined by the excess demands of different groups of agents, model developed by W. Brock and C. Hommes with additional variable of proportion of agents with different strategies and further...
Financial Crisis Prediction: Specification of Pre-crisis Periods in Turkey, Argentina and Thailand
Petr Hájek
Acta Oeconomica Pragensia 2005, 13(1):46-57 | DOI: 10.18267/j.aop.134
In this article is studied hypothesis, that every period (time interval) before financial crisis is distinguished by co-movement of several variables. The study is based on monthly data (that means no quarterly data, like portfolio investment, were used). This hypothesis, tested with vector autoregression (VAR), was to define period of time, in which a specific country is under permanent risk of falling from the edge to financial crisis (only waiting for the trigger). Variables used in this study are foreign liabilities of domestic banks (showing foreign exposure of banking sector), gross international reserves (usually rises before crisis, because...
Non-linear "Tuning" of Frankel's Exchange Rate Model
Aleš Michl
Acta Oeconomica Pragensia 2005, 13(1):58-62 | DOI: 10.18267/j.aop.136
In this essay I've demonstrated that there is evidence of unstable and non-linear relationship between fundamental variables and exchange rates. I have tried to "tune" Frankel's (1979) real interest differential model of exchange rate fluctuation. I have distinguished between Czech crown/Euro market and Euro/U.S. Dollar market because there is a different behaviour of market participants (FX dealers). Questionnaire surveys indicate that the interest rates play a ominant role in professionals' decision-making process on the UR/USD market. In that aspect I have extended Frankel's (1979) original RID model by allowing the constant and the coefficients...
Value-at-Risk and Dynamic Risk Measures
Zuzana Stuchlíková
Acta Oeconomica Pragensia 2005, 13(1):63-68 | DOI: 10.18267/j.aop.137
The article aims to survey recent advancements in risk management field. First a popular quantile-based risk measure Value-at-Risk (VaR), nowadays widely used to asses exposure to market and credit risk, is presented. Four different approaches are introduced, implemented and backtested on PSE index PX-50 time series. A class of so called coherent risk measures satisfying four qualities highly desired for a risk measure is propounded. As a response to VaR deficiencies several "improved" variants of VaR, some of them satisfying coherence axioms, are proposed. In the last section the motion of coherent risk measures is adapted to the multiperiod framework.
Stochastic Model of Thin Market with an Indivisible Commodity
Martin Šmíd
Acta Oeconomica Pragensia 2005, 13(1):94-100 | DOI: 10.18267/j.aop.140
In the paper, a thin market with an indivisible commodity, at which the market price is determined (by an organizer of the market) as the average price maximizing the traded volume, is modeled. Two models are presented - the first one with a finite, the second one with a possibly infinite number of participants. In both the cases, the joint distribution of the market price and the traded volume is derived.
The Fractal Market Analysis and Its Application on Czech Conditions
Tran Van Quang
Acta Oeconomica Pragensia 2005, 13(1):101-111 | DOI: 10.18267/j.aop.141
This paper reviews the theoretical concept of "Effecient Market Hypothesis" and introduces new concept of "Fractal Market Hypothesis". According to this hypothesis the returns follow a biased random walk called a Hurst persistent process which is characterized as long memory process. Testing this concept on Czech stock market index PX50, the (R/S) analysis was carried out and the Hurst exponent was calculated. It finds out that stock returns of PX50 follows a persistent Hurst process with Hurst exponent of 0,662. This is significantly different from the value for a random walk and it is corresponding to results of other researches done before.
Risk Measures and Dynamical Systems
Karel Vaníček
Acta Oeconomica Pragensia 2005, 13(1):112-118 | DOI: 10.18267/j.aop.142
The paper is concerned with the dynamic risk measures, e.g. with the estimation of the dynamic VaR and the dynamic ES. After general introduction into the problematic of risk management we describe the methods that are essential for the whole estimation and computation process. At first we introduce very popular time series ARMA-GARCH models and also comment the assumptions of the model that seems to be unrealistic. Due to this fact we introduce EVT models, specifically the POT model. The POT model is able to approximate the far ends of distribution, which are crucial for the estimation equation of quantile based measures. In the last but not least...
Multistage Stochastic Decision and Economic Processes
Vlasta Kaňková
Acta Oeconomica Pragensia 2005, 13(1):119-127 | DOI: 10.18267/j.aop.143
Economic and social phenomena develop over time, they are mostly influenced by random factors and, moreover, it is very often necessary to evaluate them simultaneously by several "objective" functions. Multistage stochastic programming problems, control Markov chains, empirical processes as well as stochastic multiobjective problems can serve to model them. We focus to cases that can be treated by multistage stochastic programming models with Markov type of dependence.
Using Metrics in Stability of Stochastic Programming Problems
Michal Houda
Acta Oeconomica Pragensia 2005, 13(1):128-134 | DOI: 10.18267/j.aop.145
Optimization techniques enter often as a mathematical tool into many economic applications. In these models, uncertainty is modelled via probability distribution that is approximated or estimated in real cases. Then we ask for a stability of solutions with respect to changes in the probability distribution. The work illustrates one of possible approaches (using probability metrics), underlying numerical challenges and a backward glance to economical interpretation.