
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).


Solution of Emission Management Problem
Šmíd, Martin ; Kozmík, Václav
Optimal covering of emissions stemming from random production is a multistage stochastic programming problem. Solving it in a usual way  by means of deterministic equivalent  is possible only given an unrealistic approximation of random parameters. There exists an efficient way of solving multistage problems  stochastic dual dynamic programming (SDDP), however, it requires the interstage independence of random parameters, which is not the case which our problem. In the paper, we discuss a modified version of SDDP, allowing for some form of interstage dependence.


Two Algorithms for Riskaverse Reformulation of Multistage Stochastic Programming Problems
Šmíd, Martin ; Kozmík, Václav
Many reallife applications lead to riskaverse multistage stochastic problems, therefore effective solution of these problems is of great importance. Many tools can be used to their solution (GAMS, CoinOR, APML or, for smaller problems, Excel), it is, however, mostly up to researcher to reformulate the problem into its deterministic equivalent. Moreover, such solutions are usually onetime, not easy to modify for different applications. We overcome these problems by providing a frontend software package, written in C++, which enables to enter problem definitions in a way close to their mathematical definition. Creating of a deterministic equivalent (and its solution) is up to the computer. In particular, our code is able to solve linear multistage with Multiperiod MeanCVaR or Nested MeanCVaR criteria. In the present paper, we describe the algorithms, transforming these problems into their deterministic equivalents.


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 frequentbatch auctions. We model the markets using the agentbased modeling approach. There are two exchanges on which one asset is being traded by zerointelligence (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.


Multiperiod Factor Model of a Loan Portfolio
Šmíd, Martin ; Dufek, J.
We construct a general dynamic model of losses of a large loan portfolio, secured by collaterals. In the model, the wealth of a debtor and the price of the corresponding collateral depend each on two factors: a common one, having a general distribution, and an individual one, following an AR(1) process. The default of a loan happens if the wealth stops to be su cient for repaying the loan. We show that the mapping transforming the common factors into the probability of default (PD) and the loss given default (LGD) is onetoone twice continuously differentiable. As the transformation is not analytically tractable, we propose a numerical technique for its computation and demonstrate its accuracy by a numerical study.\nWe show that the results given by our multiperiod model may differ signi cantly from\nthose resulting from singleperiod models, and demonstrate that our model naturally replicates\nthe empirically observed decrease of PDs within a portfolio in time. In addition, we give a formula for the overall loss of the portfolio and, as an example of its application, we formulate a simple optimal scoring decision problem and discuss its solution.


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 gametheoretical 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 nonneglectable probability, behave in a way that contradicts perfect rationality. This...


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 wellknown 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...


Bayesian modeling of market price using autoregression model
Šindelář, Jan ; Kárný, Miroslav (advisor) ; Pawlas, Zbyněk (referee) ; Šmíd, Martin (referee)
1 Bayesian modeling of market price using autoregression model 1Šindelář Jan Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Miroslav Kárný, DrSc. Abstract: In the thesis we present a novel solution of Bayesian filtering in autoregression model with Laplace distributed innovations. Estimation of regression models with lep tokurtically distributed innovations has been studied before in a Bayesian framework [2], [1]. Compared to previously conducted studies, the method described in this article leads to an exact solution for density specifying the posterior distribution of parameters. Such a solution was previously known only for a very limited class of innovation distributions. In the text an algorithm leading to an effective solution of the problem is also proposed. The algorithm is slower than the one for the classical setup, but due to increasing com putational power and stronger support of parallel computing, it can be executed in a reasonable time for models, where the number of parameters isn't very high. Keywords: Bayesian, Autoregression, Optimal Trading, Time Series References [1] P. Congdon. Bayesian statistical modelling. Wiley, 2006. [2] A. Zellner. Bayesian and NonBayesian analysis of the regression model with multivari ate Studentt error term. Journal...


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).


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.
