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Bimodality testing of the stochastic cusp model
Voříšek, Jan
Multimodal distributions are popular in many areas: biology (fish and shark population), engineering (material collapse under pressure, stability of ships), psychology (attitude transitions), physics (freezing of water) etc. There were a few attempts to utilize multimodal distributions in financial mathematics as well. Cobb et al. described a class of multimodal distributions belonging to the exponential family, which has unique maximum likelihood estimators and showed a connection to the stationary distribution of the stochastic cusp catastrophe model. Moreover was shown, how to identify bimodality for given parameters of the stochastic cusp model using the sign of Cardans discriminant. A statistical test for bimodality of the stochastic cusp model using maximum likelihood estimates is proposed in the paper as well as the necessary condition for bimodality which can be used for s simplified testing to reject bimodality. By proposed methods is tested the bimodality of exchange rate between USD and GBP in the periods within the years 1975 - 2014.
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Determinants of Stocks' Choice in Portfolio Competitions
Šmíd, Martin ; Kuběna, Aleš Antonín
We study investment competitions in which the players invest a virtual amount of money into financial asset and those with highest returns, measured by the actual prices, are rewarded by fixed prizes. We show that the competition, seen as a game, lacks a pure equilibrium and that the ``max-min'' solution of the game lies in the extremal point of the feasible set having maximal probability of victory. We show further that if a mixed equilibrium exists then its atoms lie exactly in the extremal points with a non-zero probability of victory and its weights are close to corresponding probabilities of victory. We analyse empirically a portfolio competition held recently by the Czech portal ``lidovky.cz''; we find that the majority of people do not behave according to the game-theoretic conclusions. Consequently, searching for factors influencing a choice of particular stocks, we find that the participants' choice may be explained by several stock traits to a certain extent. We also show that participants tend to choose negatively diversified portfolios.
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What the Data Say about the Effects of Fiscal Policy in the Czech Republic?
Baxa, Jaromír
In this paper, we provide the estimates of the fiscal multiplier in the Czech economy, based on the methodology of the fiscal VAR. The basic idea, adding fiscal variables into the macroeconomic VAR model, follows Blanchard and Perotti (2002). For estimation of our model, we utilize the dataset with quarterly data on a sample from the first quarter of 1998 to the second quarter of 2009. Our main results are as follows. Firstly, government expenditures have a positive and significant impact on the GDP. By contrast, a response of GDP on a shock to government revenues is slightly negative and in most specifications not significant. Secondly, these results are robust to various sensitivity checks. Consequently, the restoration of sustainable fiscal policy should focus rather on the revenues side than in the government expenditures, since a significant cut in government spending would probably have slowed down economic growth. Finally, we should note, that uncertainty connected with our results is large, namely in comparison with existing studies on the effects of monetary policy.
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Portfolio competitions and rationality
Kuběna, Aleš Antonín ; Šmíd, Martin
We study investment competitions in which the players with highest achieved returns are rewarded by fixed prizes. We show that, under realistic assumptions, a game the participants play lacks a pure equilibrium and that the ``max-min'' solution of the game lies in one of the extremal points of the feasible set, namely in the one having maximal probability that the portfolio return falls into its normal cone. We analyse empirically a portfolio competition held recently by the Czech portal ``lidovky.cz''; we find that the majority of people do not behave according to the game-theoretic conclusions. Consequently, searching for factors influencing a choice of particular stocks, we find that that the only significant determinant of the choice is a size of the stock's issuer.
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Multifractal Height Cross-Correlation Analysis
Krištoufek, Ladislav
We introduce a new method for detection of long-range cross- correlations and cross-multifractality – multifractal height cross-correlation analysis (MF-HXA). MF-HXA is a multivariate generalization of the height- height correlation analysis. We show that long-range cross-correlations can be caused by a mixture of the following – long-range dependence of separate processes and additional scaling of covariances between the processes. Simi- lar separation applies for cross-multifractality – standard separation between distributional properties and correlations is enriched by division of correlations between auto-correlations and cross-correlations. We further apply the method on returns and volatility of NASDAQ and S&P500 indices as well as of Crude and Heating Oil futures and uncover some interesting results.
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Modeling multivariate volatility using wavelet-based realized covariance estimator
Baruník, Jozef ; Vácha, Lukáš
Abstract. Study of the covariation have become one of the most active and successful areas of research in the time series econometrics and economic forecasting during the recent decades. Our work brings complete theory for the realized covariation estimation generalizing current knowledge and bringing the estimation to the time-frequency domain for the first time. The results generalize the popular realized volatility framework by bringing the robustness to noise as well jumps and ability to measure the realized covariance not only in time but also in frequency domain. Noticeable contribution is brought also by the application of the presented theory. Our time-frequency estimators bring not only more efficient estimates, but decomposes the realized covariation into arbitrarily chosen investment horizons. Results thus bring better understanding of the dynamics of dependence between the stock markets.
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A Simple Decision Problem of a Market Maker
Šmíd, Martin
We formulate a simple decision model of a market maker maximizing an utility from his consumption. We reduce the dimensionality of the problem to one. We nd that, given our setting, the quotes set by the market maker depend on the inventory of the traded asset but not on the amount of cash held by the market maker.
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Fiscal developments and financial stress: a threshold VAR analysis
Baxa, Jaromír ; Afonso, Antonio ; Slavík, M.
We use a threshold VAR analysis to study whether the effects of fiscal policy on economic activity differ depending on financial market conditions. In particular, we investigate the possibility of a non-linear propagation of fiscal developments according to different financial market stress regimes. More specifically we employ a quarterly dataset, for the U.S., the U.K., Germany and Italy, for the period 1980:4-2009:4, encompassing macro, fiscal and financial variables. The results show that (i) the use of a nonlinear framework with regime switches is corroborated by nonlinearity tests; (ii) the responses of economic growth to a fiscal shock are mostly positive in both financial stress regimes; (iii) financial stress has a negative effect on output growth and worsens the fiscal position; (iv) the nonlinearity in the response of output growth to a fiscal shock is mainly associated with different behaviour across regimes; (v) the size of the fiscal multipliers is higher than average in the last crisis.
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Dynamic Model of Losses of Creditor with a Large Mortgage Portfolio
Šmíd, Martin ; Gapko, Petr
We propose a dynamic model of mortgage credit losses. We assume borrowers to hold assets covering the instalments and to own a real estate which serves as a collateral; both the value of the assets and the price of the estate follow general stochastic processes driven by common and individual factors. We describe the correspondence between the common factors, the percentage of defaults and the loss given default and we suggest a procedure of econometric estimation of the model.
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