Financial Econometrics and Empirical Market Microstructure
Quality Analysis of the Models
Stylized facts are a good test for the identification of model quality, but another
important aspect is parity of basic market characteristics:
1. Returns. It is a well-known fact that simple Brownian motion does not allow the generation of heavy tails of distribution. The ZI model can generate fat tails, but the MF and Daniels models (in our case) can generate more heavy tails than in reality. It is interesting that MFWC generated returns, but without heavy tails (Fig. 10).
2. Distribution of spread. Farmer et al. (2005, 2006) in their research concentrated on spread. The spread of our model is not like the empirical one, but with heavy tails in their distribution (Fig. 11).
3. Cancellation time. The order cancellation process plays an important role in asset pricing, so it is important that its lifetime has heavy tails. The order cancellation process in the MF model shows complicated behavior, which is conditional on different market characteristics (just this process leads to a fat tail in an order’s life) (Fig. 12).
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Achard, S., & Coeurjolly, J.-F. (2010). Discrete variations of the fractional Brownian motion in the presence of outliers and an additive noise. Statistics Surveys, 4, 117-147.
Arbuzov, V., & Frolova, M. (2012). Market liquidity measurement and econometric modeling. Market risk and financial markets modeling. Heidelberg: Springer.
Bouchaud, J.-P., Gefen, Y., Potters, M., & Wyart, M. (2004). Fluctuations and response in financial markets: the subtle nature of ‘random’ price changes. Quantitative Finance, 4(2), 176-190.
Chakraborti, A., Toke, I., Patriarca, M., & Abergel, F. (2011). Econophysics review: II. Agent - based models. Quantitative Finance, 11(7), 1013-1041.
Daniels, M. G., Farmer, J. D., Gillemot, L., Iori, G., & Smith, E. (2003). Quantitative model of price diffusion and market friction based on trading as a mechanistic random process. Physical Review Letters, 90(10), 108102.
Farmer, J. D., Gillemot, L., Iori, G., Krishnamurthy, S., Smith, D. E., & Daniels, M. G. (2006). A random order placement model of price formation in the continuous double auction. The economy as an evolving complex system III (pp. 133-173). New York: Oxford University Press.
Farmer, J. D., Patelli, P., & Zovko, 1.1. (2005). The predictive power of zero intelligence in financial markets. Proceedings of the National Academy of Sciences of the United States of America, 102, 2254-2259.
Gu, G.-F., & Zhou, W.-X. (2009). On the probability distribution of stock returns in the Mike - Farmer model. European Physical Journal B, 67(4), 585-592.
He, L.-Y., & Wen, X.-C. (2013) Statistical Revisit to the Mike-Farmer Model: can this model capture the stylized facts in real world markets? Fractals, 21(2), 1-8. http://www. worldscientific. com/doi/abs/10.1142/S0218348X13500084
Lillo, F., & Farmer, J. D. (2004). The long memory of the efficient market. Studies in nonlinear dynamics & econometrics, 8(3), 1-33.
Lillo, F., Mike, S., & Farmer, J. D. (2005). Theory for long-memory of supply and demand. Physical Review E, 7106, 287-297.
Mike, S., & Farmer, J. D. (2008). An empirical behavioral model of liquidity and volatility. Journal of Economic Dynamics and Control, 32, 200-234.
R Core Team (2013) R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
