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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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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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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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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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Pravděpodobnostní vlastnosti spojité dvojité aukce - rovnoměrný případ
Šmíd, Martin
We study probabilistic properties of a zero intelligence model of a limit order market, very similar to those of /citet{Maslov00} and /citet{Smith03}. We (recursively) describe the distributions of the order books and the best quotes. Based on these theoretical results, a procedure for statistical inference of the model may be designed and the evolution of the process may be simulated more efficiently then by the crude simulation of all the events.
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Pravděpodobnostní vlastnosti spojité dvojité aukce - rovnoměrný případ
Šmíd, Martin
We study probabilistic properties of a zero intelligence model of a limit order market, very similar to those of Maslov [2000] and Smith at. al. [2003]. We (recursively) describe the distributions of the order books and the best quotes. Based on these theoretical results, we propose a procedure for statistical inference of the model and we show the way how to simulate the evolution of the process more efficiently then by the simulation of all the events. We prove that the price increments may be fat tailed if there is no initial order book but they are thin-tailed given a non-empty (Poisson distributed) order book. Finally, we show that, by a discretization of our model, the model of Smith et. al. [2003] is obtained and that a majority of our results is applicable to this model too.
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Predpovídání ve dvojité aukci se spojitým časem
Šmíd, Martin
Recently, the continuous double auction, i.e. the trading mechanism used in the majority of the financial markets, is the subject of an extensive study. In the present paper, a model of the continuous double auction with the completely random flow of the limit orders is studied. The main result of the paper is an approximate formula for the distribution of the market price and the traded volume at the time s given the information available at t < s.
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