Solvable stochastic dealer models for financial markets

Yamada, Kazuhiko; Takayasu, Hideki; Ito, Takatoshi; Takayasu, Misako

doi:10.1103/physreve.79.051120

Cited by 37 publications

(64 citation statements)

References 40 publications

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“…Other approaches simulate financial markets with computational economic models with different class of agents' strategies or using the statistics of buy and sell orders from the viewpoint of statistical physics [21][22][23][24][25][26][27][28].…”

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confidence: 99%

Financial Brownian Particle in the Layered Order Book Fluid and Fluctuation-Dissipation Relations

et al. 2014

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We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner-layer, the correlation is strong and with short memory while, in the outer-layer, it is weaker and with long memory. By interpreting and estimating the contribution from the outer-layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation (FDR)

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confidence: 99%

Financial Brownian Particle in the Layered Order Book Fluid and Fluctuation-Dissipation Relations

et al. 2014

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“…[18] Moreover, the PUCK model is theoretically shown to include ARCH/GARCH models as a special limit of random up-down cases, [19] and it is also known to be applicable to macro-limit behaviours of markets such as exponential or double-exponential rises of prices observed at inflation or hyperinflation. [20] Furthermore, it is shown by Takayasu et al [21] and Yamada et al [22][23][24] that repulsive market potential force is observed in an artificial market when trend-followers are the majority who predict near future market price by extending a trend-line. As the form of potential force can be determined from the data, the model is used as a real-time risk estimator of financial markets.…”

Section: Introductionmentioning

confidence: 94%

Rapid detection of the switching point in a financial market structure using the particle filter

Yura

Takayasu

Nakamura

et al. 2013

Journal of Statistical Computation and Simulation

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We apply the particle filter for the quick and accurate estimation of a switching point in a financial market based on a recently developed theoretical model, the potentials of unbalanced complex kinetics (PUCK) model, which fulfils all empirically stylized facts such as fat-tailed distribution of price changes and the anomalous diffusion in a short-time scale. We show the efficiency of an optimized driving force in particle filtering for the estimation of the parameters of the PUCK model, using a simulation study. As an example, we apply the method to the dollar-yen exchange market before and after the biggest earthquake in Japan in March 2011. With this fast and efficient estimation method, we can clearly confirm that the statistics of the time series of exchange rate changed drastically at the time of the arrival of the quake in Tokyo area, implying that the earthquake worked as a trigger for the market's switching point.

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“…This model is based on the Ising model. Moreover, other studies have investigated agencybased models focusing on dealer behavior [8] [13]. In addition to simulations, numerous studies have conducted empirical analysis using actual market data [15] [20].…”

Section: Modelmentioning

confidence: 99%

Simple stochastic order-book model of swarm behavior in continuous double auction

Ichiki

Nishinari

2015

Physica A: Statistical Mechanics and its Applications

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In this study, we present a simple stochastic order-book model for investors' swarm behaviors seen in the continuous double auction mechanism, which is employed by major global exchanges. Our study shows a characteristic called "fat tail" is seen in the data obtained from our model that incorporates the investors' swarm behaviors. Our model captures two swarm behaviors: one is investors' behavior to follow a trend in the historical price movement, and another is investors' behavior to send orders that contradict a trend in the historical price movement. In order to capture the features of influence by the swarm behaviors, from price data derived from our simulations using these models, we analyzed the price movement range, that is, how much the price is moved when it is continuously moved in a single direction. Depending on the type of swarm behavior, we saw a difference in the cumulative frequency distribution of this price movement range. In particular, for the model of investors who followed a trend in the historical price movement, we saw the power law in the tail of the cumulative frequency distribution of this price movement range. In addition, we analyzed the shape of the tail of the cumulative frequency distribution. The result demonstrated that one of the reasons the trend following of price occurs is that orders temporarily swarm on the order book in accordance with past price trends.

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Solvable stochastic dealer models for financial markets

Cited by 37 publications

References 40 publications

Financial Brownian Particle in the Layered Order Book Fluid and Fluctuation-Dissipation Relations

Financial Brownian Particle in the Layered Order Book Fluid and Fluctuation-Dissipation Relations

Rapid detection of the switching point in a financial market structure using the particle filter

Simple stochastic order-book model of swarm behavior in continuous double auction

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