Template-Type: ReDIF-Article 1.0 Author-Name: Roman Binter Author-Name: Lukáš Vácha Title: Local Stability and Bifurcations in Kaldor Model Abstract: 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. Keywords: economic dynamics, bifurcations, Kaldor model Classification-JEL: C62, E12, E32 Pages: 10-20 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=123.pdf File-URL: http://www.vse.cz/aop/123 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:123:p:10-20 Template-Type: ReDIF-Article 1.0 Author-Name: Petr Kadeřábek Title: Choice between the Discrete and Continuous Models in Economic Applications and Its Implications Abstract: 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). We derive a closed form formula that says if the equilibrium point in a system with a particular step length is stable or not and some implications about the stability of the same system with different step lengths. As a special case we get a relationship between stability of a discrete model and the corresponding continuous model where a difference was substituted by a derivative. Keywords: stability, discrete models, continuous models Classification-JEL: C62 Pages: 21-26 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=124.pdf File-URL: http://www.vse.cz/aop/124 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:124:p:21-26 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Kodera Author-Name: Miloslav Vošvrda Author-Name: Karel Sladký Title: A Small-Open-Economy Model and Endogenous Money Stock Abstract: 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. Keywords: non-linear dynamic model, money market dynamics, uncovered interest rate, exchange rate dynamics, limit cycle Classification-JEL: E44 Pages: 27-34 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=125.pdf File-URL: http://www.vse.cz/aop/125 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:125:p:27-34 Template-Type: ReDIF-Article 1.0 Author-Name: Jaroslav Brada Title: Risk Quantification - Early History of Option Pricing Abstract: 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. Keywords: option pricing, Prague Stock Exchange, option contracts Classification-JEL: G19, N13 Pages: 35-46 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=128.pdf File-URL: http://www.vse.cz/aop/128 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:128:p:35-46 Template-Type: ReDIF-Article 1.0 Author-Name: Dita Fuchsová Title: Performance of Selected Models with Heterogeneous Expectation Formation Abstract: 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 extended D. Goldbaum's model. Statistical properties of the time series of S&P 500 index are compared with the price time series generated by these models. This can be done due to chaotic price behaviour, which occurs for partially estimated, partially selected model values of parameters in these nonlinear dynamical systems. The results show that the third model achieves the best performance. This model is the most complex one and thus the most closely to reality but at the expense of mathematical tractability. Keywords: financial markets, heterogeneous agents, asset pricing Classification-JEL: G12 Pages: 47-56 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=129.pdf File-URL: http://www.vse.cz/aop/129 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:129:p:47-56 Template-Type: ReDIF-Article 1.0 Author-Name: Petr Hájek Title: Financial Crisis Prediction: Specification of Pre-crisis Periods in Turkey, Argentina and Thailand Abstract: 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 of central bank's defense against appreciation pressures caused by capital inflow), domestic credit (showing domestic indebtedness, in the study, this variable was lagged by 3 months) and profitability comparison with S&P 500 index in dollar recounted domestic main asset market indices. Studied countries were: Turkey, Argentina and Thailand. In every studied case, there was found several months-to-years lasting period, that confirmed accuracy of co-movement hypothesis at 1%level of significance and, also, asset market bubbles in those pre-crisis periods were found. Keywords: financial crisis prediction, vector autoregression, asset markets, bubbles Classification-JEL: C52, E61, F32 Pages: 57-69 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=134.pdf File-URL: http://www.vse.cz/aop/134 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:134:p:57-69 Template-Type: ReDIF-Article 1.0 Author-Name: Aleš Michl Title: Non-linear "Tuning" of Frankel's Exchange Rate Model Abstract: 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 for the short and long term interest rates to switch, depending on the value of the state variable. It has improved the fit of Frankel's model. On the CZK/EUR market, questionnaire surveys indicated that trade balance plays a dominant role in FX dealer's decision-making process. I suggested extending the model with trade balance variable as an approximation for income. Unfortunately there are no good time-series available for to strongly authenticate this idea in a way of non-linearity. But generally speaking, it seems that non-linear modelling of exchange rates is able to improve our understanding of exchange rate determination. Keywords: frankel, non-linearity, exchange rate Classification-JEL: C42, F31 Pages: 70-81 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=136.pdf File-URL: http://www.vse.cz/aop/136 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:136:p:70-81 Template-Type: ReDIF-Article 1.0 Author-Name: Zuzana Stuchlíková Title: Value-at-Risk and Dynamic Risk Measures Abstract: 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. Keywords: value-at-risk, coherent risk measure, dynamic risk measure Classification-JEL: C49 Pages: 82-93 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=137.pdf File-URL: http://www.vse.cz/aop/137 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:137:p:82-93 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Šmíd Title: Stochastic model of thin market with an indivisible commodity Abstract: 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. Keywords: thin market, market price, traded volume, stochastic models Classification-JEL: C65 Pages: 94-100 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=140.pdf File-URL: http://www.vse.cz/aop/140 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:140:p:94-100 Template-Type: ReDIF-Article 1.0 Author-Name: Tran Van Quang Title: The Fractal Market Analysis nad Its Application on Czech Conditions Abstract: 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. Keywords: fractal market hypothesis, Hurst exponent, Hurst persistent process Classification-JEL: E44 Pages: 101-111 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=141.pdf File-URL: http://www.vse.cz/aop/141 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:141:p:101-111 Template-Type: ReDIF-Article 1.0 Author-Name: Karel Vaníček Title: Risk Measures and Dynamical Systems Abstract: 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 paragraph there is direct estimation of both the dynamic VaR and the dynamic ES. In the last paragraph we discuss possible shortcomings of the proposed model for longer time horizon of prediction and the topic for possible research is indicated. Keywords: GARCH, EVT, VaR; ES. Classification-JEL: G30 Pages: 112-118 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=142.pdf File-URL: http://www.vse.cz/aop/142 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:142:p:112-118 Template-Type: ReDIF-Article 1.0 Author-Name: Vlasta Kaňková Title: Multistage Stochastic Decision and Economic Processes Abstract: 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. Keywords: economic processes, multistage stochastic programming, Markov dependence Classification-JEL: C44 Pages: 119-127 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=143.pdf File-URL: http://www.vse.cz/aop/143 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:143:p:119-127 Template-Type: ReDIF-Article 1.0 Author-Name: Michal Houda Title: Using Metrics in Stability of Stochastic Programming Problems Abstract: 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. Keywords: stochastic programming, quantitative stability, Wasserstein metrics, Kolmogorov metrics, simulation study Classification-JEL: C44 Pages: 128-134 Volume: 2005 Issue: 1 Year: 2005 File-URL: http://www.vse.cz/aop/download.php?jnl=aop&pdf=145.pdf File-URL: http://www.vse.cz/aop/145 File-Format: text/html Handle: RePEc:prg:jnlaop:v:2005:y:2005:i:1:id:145:p:128-134