Overview 2006-2007. A. De Martino, I. Giardina, E. Marinari, I. Perez Castillo, A. Tedeschi , M. Virasoro. Laureati/Laureandi. Riccardo Di Clemente (Laurea triennale, fin. 2/2006) : on Nash equilibria of Minority Games (A. De Martino, M.A. Virasoro)
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A. De Martino, I. Giardina, E. Marinari, I. Perez Castillo, A. Tedeschi, M. Virasoro
N.B. ( ) is a tool to interpolate between two market regimes: agents change their conduct at some threshold value ( ).
Excess Demands Time Series
RW + linear force (attractive or repulsive):
That force must be the gradiente of a quadratic potential (as in real data)
Trascurando l’effetto della liquidita’, si ha che l’incremento
di prezzo e’ proprio dato da:
Un agente che basa le sue previsioni sulla ipotesi di linearita’, avra’ che il suo valore atteso dell’incremento di prezzo sara’ dato da:
Cio’ vuol dire che gli agenti danno un peso maggiore ai
cambiamenti di peso piu’ recenti.
Tali agenti hanno un comportamento assai piu’ ricco di
semplici agenti minority o majority, che quindi si puo’ ben
descrivere con i nostri modelli ‘misti’.
The original model
The payoff becomes
Agents Memory is time steps.
The role of risk in choosing the asset: complex market structure.
- Bianconi, De Martino, Ferreira, Marsili (2006)
Can agent detect meaningful signals?
- De Martino, Tedeschi, Virasoro (in preparation)
We analyze real data about firm size, in order to validate simple money-exchange models and other ABM. We study the AIDA database, containing all data concerning Italian firms from 1996 to 2003. We concentrate on the quantities more relevant for our analysis, i.e. quantities that are directly related to the firm growth: the capital K, the added value VA, the worker number L and the asset A.
More precisely, we examine the distribution of each of the above indicators and the associated Boltzmann function H, defined as
Where for the theoretical quantities we consider: with
We consider high frequency data of the New York Stock Exchange, in particular the trades extracted from the TAQ database. The dataset contains a record of every transaction that took place during the period January 1995 – December 2003.
In order to get rid of the effect of opening and closing auctions, we analyze just the transactions occurred between 9.30 am and 15.58 pm.
We limit our analysis to stocks with more than 6000 daily transactions, and in particular to the 30 DJIA stocks.
We divide every trading day in T time intervals of the same length, such that a sufficient trade number is present in each of them.
We evaluate standard deviation of log – returns (volatility) and trade number (activity) in each interval. We average over the whole month (20 trading days).
Thus, we have T volatility values and T activity values for each month, over which we can compute correlations and perform the hypothesis tests.
The above analysis was repeated for different time intervals, different fluctuation evaluating criteria, and different hypothesis tests.
-Tedeschi, Scalas, Nicodemi, Di Matteo, Aste (in preparation)
Activity, volatility and simple money-exchange models and other ABM. We study the AIDA database, containing all data concerning Italian firms from 1996 to 2003. We concentrate on the quantities more relevant for our analysis, i.e. quantities that are directly related to the firm growth: the capital K, the added value VA, the worker number L and the asset A.
Absolute fluctuations vs.
time, and scatter-plot of
activity and volatility
Istogramma dei valori delle correlazioni significative
(circa 70% del totale)