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).


Fig. 10 Distribution of minute returns of analyzing models



Fig. 11 Spread distribution of analyzing models



lifetime of order

——– Empirical ————- Daniels…………. MF————— Upgrade

Fig. 12 Order lifetime distribution of analyzing models



We construct and estimate the parameters of two well-known models: Daniels and Mike-Farmer. During the process of the estimation of parameters, we find that distributions of price and probability of cancellation are conditional on the number of orders in the order book being quite different from the MF model. It is important that this model is very sensitive to small details in realization and small bugs in the code. Parameters being not carefully estimated can lead to a significant worsening of model results. We have tried to upgrade the model for our data, including an additional parameter for the




Подпись: order cancellation process and fitting prices using two power-law distributions with t-Student’s center. The upgrade model for our sample shows the best results. It is important that the model represents only the microstructure of the market of Aeroflot stocks in January and cannot be spread to other instruments.


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