×

Analysis of a decision model in the context of equilibrium pricing and order book pricing. (English) Zbl 1402.91163

Summary: An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its parameter dependence within a supply-demand balance setting. We find realistic behavior in a wide parameter range. Second, we embed our decision model in an order book setting. Here, we observe interesting features which are not present in the equilibrium pricing scheme. In particular, we find a nontrivial behavior of the order book volumes which reminds of a trend switching phenomenon. Thus, the decision making model alone does not realistically represent the trading and the stylized facts. The order book mechanism is crucial.

MSC:

91B25 Asset pricing models (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Mas-Colell, A.; Whinston, M. D.; Green, J. R., Microeconomic theory, (1995), Oxford University Press · Zbl 1256.91002
[2] Dixon, H. D., Surfing economics, (2001), Palgrave Macmillan
[3] Bornholdt, S., Expectation bubbles in a spin model of markets: intermittency from frustration across scales, Internat. J. Modern Phys. C, 12, 5, 667-674, (2001)
[4] Kaizoji, T.; Bornholdt, S.; Fujiwara, Y., Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents, Physica A, 316, 441-452, (2002) · Zbl 1001.91037
[5] Kim, Y.; Kim, H.-J.; Yook, S.-H., Agent-based spin model for financial markets on complex networks: emergence of two-phase phenomena, Phys. Rev. E, 78, 3, 1-6, (2008)
[6] Friedman, D.; Rust, J., The double auction market, (1993), The Advanced Book Program
[7] Johnson, B., Algorithmic trading & DMA, (2010), 4Myeloma Press
[8] Chakraborti, A.; Toke, I. M.; Patriarca, M.; Abergel, F., Econophysics review: I. empirical facts, Quant. Finance, 11, 7, 991-1012, (2011)
[9] Mandelbrot, B., The variation of certain speculative prices, J. Bus., 36, 4, 394-419, (1963)
[10] Plerou, V.; Gopikrishnan, P.; Nunes Amaral, L. A.; Meyer, M.; Stanley, H. E., Scaling of the distribution of price fluctuations of individual companies, Phys. Rev. E, 60, 6 Pt A, 6519-6529, (1999)
[11] Mantegna, R. N.; Stanley, H. E., Introduction to econophysics: correlations and complexity in finance, (1999), Cambridge University Press · Zbl 1138.91300
[12] Plerou, V.; Stanley, H. E.; Gabaix, X.; Gopikrishnan, P., On the origin of power-law fluctuations in stock prices, Quant. Finance, 4, 1, 11-15, (2004) · Zbl 1405.91567
[13] Clark, P. K., A subordinated stochastic process model with finite variance for speculative prices, Econ. Soc., 41, 1, 135-155, (1973) · Zbl 0308.90011
[14] Arthur, W. B.; Holland, J. H.; LeBaron, B.; Palmer, R.; Tayler, P., Asset pricing under endogenous expectations in an artificial stock market, (Arthur, W. B.; Durlauf, S. N.; Lane, D. H., The Economy as an Evolving Complex System II, Vol. 1001, (1996), Addison-Wesley), 15-44
[15] Mandelbrot, B., Fractals and scaling in finance, (1997), Springer · Zbl 1005.91001
[16] Sornette, D., Multiplicative processes and power laws, Phys. Rev. E, 57, 4, 4811-4813, (1998)
[17] Lux, T.; Marchesi, M., Scaling and criticality in a stochastic multi-agent model of a financial market, Nature, 397, 498-500, (1999)
[18] Challet, D.; Chessa, A.; Marsili, M.; Zhang, Y.-C., From minority games to real markets, Quant. Finance, 1, 1, 9, (2000)
[19] Farmer, J. D.; Gillemot, L.; Lillo, F.; Mike, S.; Sen, A., What really causes large price changes?, Quant. Finance, 4, 4, 383-397, (2004) · Zbl 1405.91738
[20] Gabaix, X.; Gopikrishnan, P.; Plerou, V., A theory of power-law distributions in financial market fluctuations, Nature, 423, 267-270, (2003)
[21] Farmer, J. D.; Lillo, F., On the origin of power-law tails in price fluctuations, Quant. Finance, 4, 1, C7-C11, (2004) · Zbl 1405.91551
[22] Cohen, K. J.; Maier, S. F.; Schwartz, R. A.; Whitcomb, D. K., A simulation model of stock exchange trading, Simulation, 41, 5, 181-191, (1983)
[23] Kim, G.; Markowitz, H., Investment rules, margin, and market volatility, J. Portf. Manage., 16, 1, 45-52, (1989)
[24] Frankel, J. A.; Froot, K. A., Explaining the demand for dollars: international rates of return and the expectations of chartists and fundamentalists, (Chambers, R.; Paarlberg, P., Agriculture, Macroeconomics, and the Exchange Rate, (1988), Westview Press)
[25] Chiarella, C., The dynamics of speculative behaviour, Ann. Oper. Res., 37, 1, 101-123, (1992) · Zbl 0777.90008
[26] Beltratti, A.; Margarita, S., Evolution of trading strategies among heterogeneous artificial economic agents, (Meyer, J.-A.; Roitblat, H. L.; Wilson, S. W., From Animals to Animats 2, (1993)), 494-501
[27] Levy, M.; Levy, H.; Solomon, S., A microscopic market model of the stock market, Econ. Lett., 45, 103-111, (1994) · Zbl 0800.90163
[28] Lux, T., Time variation of second moments from a noise trader/infection model, J. Econom. Dynam. Control, 22, 1, 1-38, (1997) · Zbl 0897.90072
[29] Mike, S.; Farmer, J. D., An empirical behavioral model of liquidity and volatility, J. Econom. Dynam. Control, 32, 1, 200-234, (2008)
[30] Gu, G.-F.; Zhou, W.-X., Emergence of long memory in stock volatility from a modified mike-farmer model, Europhys. Lett., 86, 4, 48002, (2009)
[31] B. LeBaron, Building the Santa Fe artificial stock market, 2002.
[32] Ehrentreich, N., Agent-based modeling: the Santa Fe institute artificial stock market model revisited, (2007), Springer · Zbl 1141.91014
[33] Alfi, V.; Cristelli, M.; Pietronero, L.; Zaccaria, A., Minimal agent based model for financial markets I, Eur. Phys. J. B, 67, 385-397, (2009) · Zbl 1188.91132
[34] Alfi, V.; Cristelli, M.; Pietronero, L.; Zaccaria, A., Minimal agent based model for financial markets II, Eur. Phys. J. B, 67, 399-417, (2009) · Zbl 1188.91133
[35] Kreps, M., A course in microeconomic theory, (1990), Princeton University Press
[36] Giardina, I.; Bouchaud, J.-P.; Mézard, M., Microscopic models for long ranged volatility correlations, Physica A, 299, 28-39, (2001) · Zbl 0974.91018
[37] Preis, T.; Golke, S.; Paul, W.; Schneider, J., Statistical analysis of financial returns for a multiagent order book model of asset trading, Phys. Rev. E, 76, 1, 1-13, (2007)
[38] Schmitt, T. A.; Schäfer, R.; Münnix, M. C.; Guhr, T., Microscopic understanding of heavy-tailed return distributions in an agent-based model, Europhys. Lett., 100, 38005, (2012)
[39] Török, J.; Iniguez, G.; Yasseri, T.; San Miguel, M.; Kaski, K.; Kertesz, J., Opinions, conflicts, and consensus: modeling social dynamics in a collaborative environment, Phys. Rev. Lett., 110, 088701, (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.