Abstract
A model for financial market activity should reproduce the several stylized facts that have been observed to be invariant across different markets and periods. Here we present a mean-field model of agents trading a particular asset, where their decisions (to buy or to sell or to hold) is based exclusively on the price history. As there are no direct interactions between agents, the price (computed as a function of the net demand, i.e., the difference between the numbers of buyers and sellers at a given time) is the sole mediating signal driving market activity. We observe that this simple model reproduces the long-tailed distribution of price fluctuations (measured by logarithmic returns) and trading volume (measured in terms of the number of agents trading at a given instant), that has been seen in most markets across the world. By using a quenched random distribution of a model parameter that governs the probability of an agent to trade, we obtain quantitatively accurate exponents for the two distributions. In addition, the model exhibits volatility clustering, i.e., correlation between periods with large fluctuations, remarkably similar to that seen in reality. To the best of our knowledge, this is the simplest model that gives a quantitatively accurate description of financial market behavior.
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References
Farmer J D, Shubik M Smith E (2005) Is economics the next physical science? Physics Today 58(9): 37–42
Cont R (2001) Empirical properties of asset returns: stylized facts and statistical issues, Quant. Fin. 1: 223:236
Lux T (1996) The stable Paretian hypothesis and the frequency of large returns: An examination of major German stocks, Appl. Fin. Econ. 6: 463–475
Gopikrishnan P, Meyer M, Amaral L A N, Stanley H E (1998) Inverse cubic law for the probability distribution of stock price variations, Eur. Phys. J. B 3: 139–140
Gopikrishnan P, Plerou V, Amaral L A N, Meyer M, Stanley H E (1999) Scaling of fluctuations of financial market indices, Phys. Rev. E 60: 5305–5316
Pan R K, Sinha S (2007) Self-organization of price fluctuation distribution in evolving markets, Europhys. Lett. 77: 58004
Pan, R K, Sinha S (2008) Inverse-cubic law of index fluctuation distribution in Indian markets, Physica A 387: 2055–2065
Gopikrishnan P, Plerou V, Gabaix X, Stanley H E (2000) Statistical properties of share volume traded in financial markets. Phys. Rev. E 62: R4493–R4496
Liu Y, Gopikrishnan P, Cizeau P, Meyer M, Peng C-K, Stanley H E (1999) The statistical properties of the volatility of price fluctuations. Phys. Rev. E 60: 1390–1400
Lux T, Marchesi M (1999) Scaling and criticality in a stochastic multi-agent model of a financial market, Nature 397: 498–500
Chowdhury D, Stauffer D (1999) A generalised spin model of financial markets, Eur. Phys. J. B 8: 477–482
Cont R, Bouchad J P (2000) Herd behavior and aggregate fluctuations in financial markets, Macroecon. Dyn. 4: 170–196
Bornholdt S (2001) Expectation bubbles in a spin model of markets: Intermittency from frustration across scales, Int. J. Mod. Phys. C 12: 667–674
Iori G (2002) A microsimulation of traders activity in the stock market: the role of heterogeneity, agents’ interaction and trade frictions, J. Econ. Behav. Organ. 49:269–285
Bachelier L (1900) Théorie de la spéculation, Ann. Sci. École Norm. Sup. Sér 3 17: 21–86
Potters M, Bouchaud J-P (2003) More statistical properties of order books and price impact, Physica A 324: 133–140
Alfi V, Coccetti F, Marotta M, Pietronero L, Takayasu M(2006) Hidden forces and fluctuations from moving averages: A test study, Physica A 370: 30–37
Newman M E J (2005) Power laws, Pareto distributions and Zipf’s law, Contemp. Phys. 46: 323–351
Hill B M (1975) A simple approach to inference about tail of a distribution, Ann. Stat. 3: 1163–1174
Fama E (1970) Efficient capital markets: A review of theory and empirical work, J. Finance 25: 383–417
Kaizoji T (2006) A precursor of market crashes: Empirical laws of Japan’s internet bubble, Eur. Phys. J. B 50: 123–127
Yang J S, Chae S, Jung W S, Moon H T (2006) Microscopic spin model for the dynamics of the return distribution of the Korean stock market index, Physica A 363: 377–382
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Vikram, S.V., Sinha, S. (2010). A Mean-Field Model of Financial Markets: Reproducing Long Tailed Distributions and Volatility Correlations. In: Basu, B., Chakravarty, S.R., Chakrabarti, B.K., Gangopadhyay, K. (eds) Econophysics and Economics of Games, Social Choices and Quantitative Techniques. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-1501-2_12
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DOI: https://doi.org/10.1007/978-88-470-1501-2_12
Publisher Name: Springer, Milano
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