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Selected Publications
Tobias Preis, Sebastian Golke, Wolfgang Paul, and Johannes J. Schneider,
Multi-agent-based Order Book Model of financial markets,
Europhysics Letters 75, 510-516 (2006)
Abstract. We introduce a simple model for simulating financial markets, based on an order book, in which several agents trade one asset at a virtual exchange continuously. For a stationary market the structure of the model, the order flow rates of the different kinds of order types and the used price time priority matching algorithm produce only a diffusive price behavior. We show that a market trend, i.e. an asymmetric order flow of any type, leads to a non-trivial Hurst exponent for the price development, but not to "fat-tailed" return distributions. When one additionally couples the order entry depth to the prevailing trend, also the stylized empirical fact of "fat tails" can be reproduced by our Order Book Model.
[ PDF ]
Tobias Preis, Sebastian Golke, Wolfgang Paul, and Johannes J. Schneider,
Statistical analysis of financial returns for a multiagent order book model of asset trading,
Physical Review E 76, 016108 (2007)
Abstract. We recently introduced a realistic order book model [T. Preis et al., Europhys. Lett. 75, 510 (2006)] which is able to generate the stylized facts of financial markets. We analyze this model in detail, explain the consequences of the use of different groups of traders, and focus on the foundation of a nontrivial Hurst exponent based on the introduction of a market trend. Our order book model supports the theoretical argument that a nontrivial Hurst exponent implies not necessarily long-term correlations. A coupling of the order placement depth to the market trend can produce fat tails, which can be described by a truncated Lévy distribution.
[ PDF ]
Tobias Preis, Wolfgang Paul, and Johannes J. Schneider,
Fluctuation patterns in high-frequency financial asset returns,
Europhysics Letters 82, 68005 (2008)
Abstract. We introduce a new method for quantifying pattern-based complex short-time correlations of a time series. Our correlation measure is 1 for a perfectly correlated and 0 for a random walk time series. When we apply this method to high-frequency time series data of the German DAX future, we find clear correlations on short time scales. In order to subtract trivial autocorrelation parts from the pattern conformity, we introduce a simple model for reproducing the antipersistent regime and use alternatively level 1 quotes. When we remove the pattern conformity of this stochastic process from the original data, remaining pattern-based correlations can be observed.
[ PDF ]
Tobias Preis, Peter Virnau, Wolfgang Paul, and Johannes J. Schneider,
GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model,
Journal of Computational Physics 228, 4468-4477 (2009)
Abstract. The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a current CPU core. An implementation of the three dimensional ferromagnetic cubic lattice Ising model on a GPU is able to generate results up to 35 times faster than on a current CPU core. As proof of concept we calculate the critical temperature of the 2D and 3D Ising model using finite size scaling techniques. Theoretical results for the 2D Ising model and previous simulation results for the 3D Ising model can be reproduced.
[ PDF ] [ Download Source Code ]
Tobias Preis, Peter Virnau, Wolfgang Paul, and Johannes J. Schneider,
Accelerated fluctuation analysis by graphic cards and complex pattern formation in financial markets,
New Journal of Physics 11, 093024 (2009)
Abstract. The compute unified device architecture is an almost conventional programming approach for managing computations on a graphics processing unit (GPU) as a data-parallel computing device. With a maximum number of 240 cores in combination with a high memory bandwidth, a recent GPU offers resources for computational physics. We apply this technology to methods of fluctuation analysis, which includes determination of the scaling behavior of a stochastic process and the equilibrium autocorrelation function. Additionally, the recently introduced pattern formation conformity (Preis T et al 2008 Europhys. Lett. 82 68005), which quantifies pattern-based complex short-time correlations of a time series, is calculated on a GPU and analyzed in detail. Results are obtained up to 84 times faster than on a current central processing unit core. When we apply this method to high-frequency time series of the German BUND future, we find significant pattern-based correlations on short time scales. Furthermore, an anti-persistent behavior can be found on short time scales. Additionally, we compare the recent GPU generation, which provides a theoretical peak performance of up to roughly 1012 floating point operations per second with the previous one.
[ PDF ]
Tobias Preis and H. Eugene Stanley,
How to Characterize Trend Switching Processes in Financial Markets,
Bulletin of the Asia Pacific Center for Theoretical Physics 23, 18-23(2009)
[ PDF ] [ Cover Image ]
Tobias Preis and H. Eugene Stanley,
Switching Phenomena in a System with No Switches,
Journal of Statistical Physics 138, 431-446 (2010)
Abstract. It is widely believed that switching phenomena require switches, but this is actually not true. For an intriguing variety of switching phenomena in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fashion. For example, financial market fluctuations are characterized by many abrupt switchings creating increasing trends ("bubble formation") and decreasing trends ("financial collapse"). Such switching occurs on time scales ranging from macroscopic bubbles persisting for hundreds of days to microscopic bubbles persisting only for a few seconds. We analyze a database containing 13,991,275 German DAX Future transactions recorded with a time resolution of 10 msec. For comparison, a database providing 2,592,531 of all S&P500 daily closing prices is used. We ask whether these ubiquitous switching phenomena have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the volatility after each switching occurs. We interpret our findings as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in transaction volume and time intervals between trades. We show that these financial market switching processes have properties similar to those of phase transitions. We suggest that the well-known catastrophic bubbles that occur on large time scales — such as the most recent financial crisis — are no outliers but single dramatic representatives caused by the switching between upward and downward trends on time scales varying over nine orders of magnitude from very large (∼ 100 days) down to very small (∼ 10 ms).
[ PDF ]
H. Eugene Stanley, Sergey V. Buldyrev, Giancarlo Franzese, Shlomo Havlin, Francesco Mallamace, Pradeep Kumar, Vasiliki Plerou, and Tobias Preis,
Correlated randomness and switching phenomena,
Physica A 389, 2880-2893 (2010)
Abstract. One challenge of biology, medicine, and economics is that the systems treated by these serious scientific disciplines have no perfect metronome in time and no perfect spatial architecture — crystalline or otherwise. Nonetheless, as if by magic, out of nothing but randomness one finds remarkably fine-tuned processes in time and remarkably fine-tuned structures in space. Further, many of these processes and structures have the remarkable feature of "switching" from one behavior to another as if by magic. The past century has, philosophically, been concerned with placing aside the human tendency to see the universe as a fine-tuned machine. Here we will address the challenge of uncovering how, through randomness (albeit, as we shall see, strongly correlated randomness), one can arrive at some of the many spatial and temporal patterns in biology, medicine, and economics and even begin to characterize the switching phenomena that enables a system to pass from one state to another. Inspired by principles developed by A. Nihat Berker and scores of other statistical physicists in recent years, we discuss some applications of correlated randomness to understand switching phenomena in various fields. Specifically, we present evidence from experiments and from computer simulations supporting the hypothesis that water’s anomalies are related to a switching point (which is not unlike the "tipping point" immortalized by Malcolm Gladwell), and that the bubbles in economic phenomena that occur on all scales are not "outliers" (another Gladwell immortalization). Though more speculative, we support the idea of disease as arising from some kind of yet-to-be-understood complex switching phenomenon, by discussing data on selected examples, including heart disease and Alzheimer disease.
[ PDF ]
Benjamin Block, Peter Virnau, and Tobias Preis,
Multi-GPU accelerated multi-spin Monte Carlo simulations of the 2D Ising model,
Computer Physics Communications 181, 1549-1556 (2010)
Abstract. A Modern Graphics Processing unit (GPU) is able to perform massively parallel scientific computations at low cost. We extend our implementation of the checkerboard algorithm for the two-dimensional Ising model [T. Preis et al., Journal of Computational Physics 228 (2009) 4468–4477] in order to overcome the memory limitations of a single GPU which enables us to simulate significantly larger systems. Using multi-spin coding techniques, we are able to accelerate simulations on a single GPU by factors up to 35 compared to an optimized single Central Processor Unit (CPU) core implementation which employs multi-spin coding. By combining the Compute Unified Device Architecture (CUDA) with the Message Parsing Interface (MPI) on the CPU level, a single Ising lattice can be updated by a cluster of GPUs in parallel. For large systems, the computation time scales nearly linearly with the number of GPUs used. As proof of concept we reproduce the critical temperature of the 2D Ising model using finite size scaling techniques.
[ PDF ] [ Download Source Code ]
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Contact Addresses:
Institute of Physics, Johannes Gutenberg University, Staudinger Weg 7, D-55099 Mainz, Germany
Artemis Capital Asset Management GmbH, Gartenstr. 14, D-65558 Holzheim, Germany
Last update on 29 July 2010
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