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Ising model in finance: from microscopic rules to macroscopic phenomena
Dvořák, Pavel ; Krištoufek, Ladislav (advisor) ; Kukačka, Jiří (referee)
The main objective of this thesis is to inspect the abilities of the Ising model to exhibit selected statistical properties, or stylized facts, that are common to a wide range of financial assets. The investigated properties are heteroskedasticity of returns, rapidly decaying linear autocorrelation, volatility clustering, heavy tails, negative skewness and non-Gaussianity of the return distribution. In the first part of the thesis, we test the presence of these stylized facts in S&P 500 daily returns over the last 30 years. The main part of the thesis is dedicated to the Ising model-based simulations and to discussion of the results. New features such as Poisson process governed lag or magnetisation dependent trading activity are incorporated in the model. We conclude that the Ising model is able to convincingly replicate most of the examined statistical properties while even more satisfactory results can be obtained with appropriate tuning. 1
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Capital Market Hypotheses and Their Statistical Implications: A Comparative Study
Petras, Petr ; Krištoufek, Ladislav (advisor) ; Křehlík, Tomáš (referee)
In this bachelor thesis we focus on different Market Hypotheses. Specifically on Efficient Market Hypothesis, Fractal Market Hypothesis and Coherent Market Hypothesis. In the first part of the work we provide description of researched hypotheses and methods used for testing. In the second part of the work we run test on time series of share markets, gold markets and currency markets and test if our hypotheses can provide explanation about price changes on those markets. For Efficient Market Hypothesis we wonder if prices are following random walk (via augmented Dickey-Fuller test), if residuals are normally distributed (via Shapiro-Wilk and Jarque-Bera tests) and if residuals are uncorrelated (via Box-Pierce test). For Fractal Market Hypothesis we are trying to find value of Hurst exponent via Rescaled Range analysis. This exponent describes if time series are persistent or not. And for Coherent Market Hypothesis we develop simple method for testing if some time periods can yield above-average revenues, thanks to increased mean and decreased standard deviation. After that we find out what are consequences of short time series and different frequencies for obtaining data points and we learn that some hypotheses describes different time periods or lengths better and are not so good for different ones. Powered...
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Ising model in finance: from microscopic rules to macroscopic phenomena
Dvořák, Pavel ; Krištoufek, Ladislav (advisor) ; Kukačka, Jiří (referee)
The main objective of this thesis is to inspect the abilities of the Ising model to exhibit selected statistical properties, or stylized facts, that are common to a wide range of financial assets. The investigated properties are heteroskedasticity of returns, rapidly decaying linear autocorrelation, volatility clustering, heavy tails, negative skewness and non-Gaussianity of the return distribution. In the first part of the thesis, we test the presence of these stylized facts in S&P 500 daily returns over the last 30 years. The main part of the thesis is dedicated to the Ising model-based simulations and to discussion of the results. New features such as Poisson process governed lag or magnetisation dependent trading activity are incorporated in the model. We conclude that the Ising model is able to convincingly replicate most of the examined statistical properties while even more satisfactory results can be obtained with appropriate tuning. 1
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