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Statistical inference of the Modified Smith?s model
Rušin, Michal ; Šmíd, Martin (advisor) ; Hlubinka, Daniel (referee)
The present work discuss the continuous double auction mechanisms and the order book models. After a brief introduction to selected models, a general model of the the continuous double auction from the thesis title is described. Further, a structure of british market data is given as well as an approach to them. Based on these data the validity of Smith Farmer's model and Cont Stoikov's model is tested in the context of general model by linear regression. Finally, based on the previous results, the own order book model is suggested and its validity tested.
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Three Essays on Credit Risk Quantification
Gapko, Petr ; Šmíd, Martin (advisor) ; Witzany, Jiří (referee) ; Tichý, Tomáš (referee) ; D'Ecclesia, Rita Laura (referee)
The dissertation thesis deals with modeling and estimating credit risk. In the thesis we particularly focus on the credit risk of retail, and more exactly mortgage, debtors. The thesis is organized into three separate papers with a common theme, which is a development of a credit risk measurement methodology from simpler enhancements of the current research to a model able to capture such details as e.g. the duration structure of the mortgage portfolio. All three papers use the same underlying dataset, a time series of the national US mortgage portfolio delinquency and foreclosure rates. As the research was done during several years, the latter parts of the thesis work with additional observations. In the first paper, we demonstrate that the current regulatory standards for credit risk quantification are based on assumptions that do not necessarily match the reality. Generalizing the well-known Vasicek's model, standing behind the Basel II, we build a model of a credit risk of a loan portfolio. The model, similarly to the Vasicek's model, decomposes the credit risk (expressed as the portfolio probability of default) into two risk factors, one common for all borrowers in the portfolio, and one individual for each single borrower. Our model involves dynamics of the common factor, which influences the...
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Comparison of continuous and frequent batch auctions
Gottlieb, Oskar ; Šmíd, Martin (advisor) ; Červinka, Michal (referee)
We simulate a fragmented market and study three types of agents and their interactions in continuous trading and frequent-batch auctions. We model the markets using the agent-based modeling approach. There are two exchanges on which one asset is being traded by zero-intelligence (ZI) traders, market makers and a latency arbitrageur. The former two agents are marked as slow traders, the arbitrageur is a fast trader - fast trader has perfect information about the market, slow traders are dependent on the (possibly lagged) NBBO information provided by the regulator. Our main metric is the surplus of ZI traders, we also measure other market's characteristics. We then simulate the market for different delays of the NBBO delay and we find that under certain conditions and until certain length, the batch auctions are beneficial to ZI traders, as they reduce the advantage and therefore the profit of the fast trader.
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ACD Model and the Czech Capital Market
Moravová, Anna ; Šmíd, Martin (advisor) ; Beneš, Viktor (referee)
This study is concerned with the autoregressive conditional duration model (ACD) and its applications on the data from the Prague Stock exchange. The ACD model is particularly suitable for the analysis of data which arrive at irregular time intervals. We treat the time between events as a stochastic process. We apply the ACD model to model the intervals between the trades with the stock of Komerčn' Banka at the Prague Stock Exchange in the year 2004. The parameters are estimated by the maximum likelihood method. Further, an extension of the ACD model - the ACD-ACM model - is studied. ACM model is used to model the discrete price changes in the stock prices. The distribution of each price change is considered to be a random variable with distribution conditional on the past price changes and other explanatory variables. The ACD-ACM model is applied to the quote data of the stock of Czech Telecom from the year 2004. The results of the calculations are compared with the results presented by Engle and Russel in their studies from the years 1998 and 2005.
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The selection drift against perfect rationality
Kuběna, Aleš ; Šmíd, Martin (advisor) ; Vlach, Milan (referee) ; Šizling, Arnošt Leoš (referee)
A direct application of game theory to conflicts and cooperation of organisms gives different theoretical predictions for their behaviour than economic models, even if the economic models are based on game theory themselves. These direct predictions are in better accordance with empirical data than the economic models. A difference is observed even if we analyse how organisms deal with sources and how they compete for sources, a problem of apparently economic nature. My thesis shows that these contradictions cannot be removed in a plausible way, even not via introducing new biological restrictions in the "economic" decision model applied to organisms, and not even via enriching the utility functions by evolutionary goals. Thus it is not satisfactory to assume rational agents who replaced a utility maximisation by the maximisation of offspring numbers. In my model, gathering of sources is used in a game-theoretical analysis as a necessary condition, but not as a sufficient condition of evolutionary sustainability. Analýza predicts that the fact whether a rational, collectively rational, altruistic, or different strategy wins in some population, is a matter of random fluctuation. In this model, agents will, with non-neglectable probability, behave in a way that contradicts perfect rationality. This...
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A verification of an approximation of the continuous double auction by a sequence of call auctions.
Kubík, Petr ; Šmíd, Martin (advisor) ; Branda, Martin (referee)
The thesis deals with two kinds of double auction - with the continuous auction and a sequence of call auctions. We explain their rules and we define their models. We present results of simulations of the both kinds of double auction - the aim is to look for the call auction with such parameters that the prices and the traded volume of the continuous auction are approximated best. Finally, in a theoretical part, we characterize the dis- tribution of the order book in the continuous auction and then we specify the joint distribution of the price and the traded volume in the call auction (the distribution of bid, ask and the traded volume given by the continuous auction may be immediately devised from the distribution of the order book).
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Maximum Return Portfolio
Palko, Maximilián ; Večeř, Jan (advisor) ; Šmíd, Martin (referee)
Classical method of portfolio selection is based on minimizing the variabi- lity of the portfolio. The Law of Large Numbers tells us that in case of longer investment horizon it should be enough to invest in the asset with the highest expected return which will eventually outperform any other portfolio. In our thesis we will suggest some portfolio creation methods which will create Maxi- mum Return Portfolios. These methods will be based on finding the asset with maximal expected return. That way we will avoid the problem of estimation errors of expected returns. Two of those methods will be selected based on the results of simulation analysis. Those two methods will be tested with the real stock data and compared with the S&P 500 index. Results of the testing suggest that our portfolios could have an application in the real world. Mainly because our portfolios showed to be significantly better than the index in the case of 10 year investment horizon. 1
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A verification of an approximation of the continuous double auction by a sequence of call auctions.
Kubík, Petr ; Šmíd, Martin (advisor) ; Branda, Martin (referee)
The thesis deals with two kinds of double auction - with the continuous auction and a sequence of call auctions. We explain their rules and we define their models. We present results of simulations of the both kinds of double auction - the aim is to look for the call auction with such parameters that the prices and the traded volume of the continuous auction are approximated best. Finally, in a theoretical part, we characterize the dis- tribution of the order book in the continuous auction and then we specify the joint distribution of the price and the traded volume in the call auction (the distribution of bid, ask and the traded volume given by the continuous auction may be immediately devised from the distribution of the order book).
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