# Replicating financial market dynamics with a simple self-organized critical lattice model

@article{Dupoyet2010ReplicatingFM, title={Replicating financial market dynamics with a simple self-organized critical lattice model}, author={Brice V. Dupoyet and H. Rudolf Fiebig and David Musgrove}, journal={Fuel and Energy Abstracts}, year={2010} }

We explore a simple lattice field model intended to describe statistical properties of high frequency financial markets. The model is relevant in the cross-disciplinary area of econophysics. Its signature feature is the emergence of a self-organized critical state. This implies scale invariance of the model, without tuning parameters. Prominent results of our simulation are time series of gains, prices, volatility, and gains frequency distributions, which all compare favorably to features of…

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#### References

SHOWING 1-10 OF 41 REFERENCES

Self-organized percolation model for stock market fluctuations

- Economics, Physics
- 1999

In the Cont–Bouchaud model [cond-mat/9712318] of stock markets, percolation clusters act as buying or selling investors and their statistics controls that of the price variations. Rather than fixing…

HERD BEHAVIOR AND AGGREGATE FLUCTUATIONS IN FINANCIAL MARKETS

- Economics, PhysicsMacroeconomic Dynamics
- 2000

We present a simple model of a stock market where a random communication structure between agents generically gives rise to heavy tails in the distribution of stock price variations in the form of an…

Herd Behavior and Aggregate Fluctuations in Financial Markets

- Economics
- 1997

We present a simple model of a stock market where a random communication structure between agents gives rise to a heavy tails in the distribution of stock price variations in the form of an…

Price Variations in a Stock Market with Many Agents

- Economics, Physics
- 1997

Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock…

Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets

- Mathematics
- 2010

We report on initial studies of a quantum field theory defined on a lattice with multi-ladder geometry and the dilation group as a local gauge symmetry. The model is relevant in the…

Stylized Facts of Daily Return Series and the Hidden Markov Model

- Mathematics
- 1998

In two recent papers, Granger and Ding (1995a,b) considered long return series that are first differences of logarithmed price series or price indices. They established a set of temporal and…

Microscopic Simulation of Financial Markets: From Investor Behavior to Market Phenomena

- Economics
- 2000

From the Publisher:
"Levy, Levy, and Solomon's Microscopic Simulation of Financial Markets points us towards the future of financial economics. If we restrict ourselves to models which can be solved…

An Introduction to Econophysics: Correlations and Complexity in Finance

- Computer Science, Economics
- 1999

Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Technical Appendix A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?

- Economics
- 2001

We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models are compared out-of-sample using DM-d exchange rate data and IBM return data, where the…

A Forecast Comparison of Volatility Models: Does Anything Beat a Garch(1,1)?

- 2004

We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models are compared out-of-sample using DM-$ exchange rate data and IBM return data, where the…