De Martino, Giardina, Tedeschi (2004)

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)
•Luca Columbu (Laurea, fin. 12/2006) : on statistical mechanics of
social choice and the Condorcet `paradox' (A. De Martino, E.
Marinari)
•Ottaviano Rosi (Laurea, fin. 4/2007) : on agent-based models of
resource-sharing networks (A. De Martino, M.A. Virasoro)
•Nicola Tamburrino (Laurea, exp. 2/2008) : on activity-volatility
correlation in NYSE stocks (A. Tedeschi, M. Nicodemi)
Generalized Minority Games with
risk-sensitive agents
• Contrarians/trend-followers are described by
minority/majority game players (rewarded when
acting in the minority/majority group).
• Our model allows to switch from one group to the
other, according to the risk perceived by the agents.
• Trend-following behavior dominates when price
movements are small, whereas traders turn to a
contrarian conduct when the market is chaotic.
-De Martino, Giardina, Tedeschi, Marsili (2004)
- De Martino, Giardina, Tedeschi (2004)
-Tedeschi, De Martino, Giardina (2005)
- Alfi, De Martino, Pietronero, Tedeschi (2006)

The payoff function is pig t 1  pig t   aig F At  :
3
2
F ( A)  A  A
3
1
0
-4
-3
-2
-1
0
1
2
3
4
-1
-2
-3
15
10
5
0
-15
-10
-5
0
5
10
15
F ( A)    A    A  A
-5
-10
-15
N.B.  (  ) is a tool to interpolate between two market regimes:

agents change their conduct at some threshold value A  1  ( A   ).
Non-Gaussian distribution of Returns
F ( A)  A  A3
Excess Demands Time Series
Case of Endogenous Information
•
In this case trend-following behavior is expected to strongly
influence the macroscopic properties, because of the bias that trends
would impose on the resulting history dynamics.
Effective Potential Model & Mixed Min-Maj Game
RW + linear force (attractive or repulsive):
That force must be the gradiente of a quadratic
potential (as in real data)
Effective Potential Model & Mixed Min-Maj Game
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’.
Grand Canonical Minority Game
The original model
• N traders (i=1,...,N)
• P information patterns (   1,..., P)
• Random strategies ai   1,1P
• Dynamics:
ni (t )  [U i (t )]  0,1
Active/inactive agents
U i (t  1)  U i (t )  ai A(t )   i

A
(
t
)

a
where
 i ni (t )
i
N  Ns  NP
 i  0 Risk averse
(speculators and producers)   0 Risk prone
i
S  
 P  
- Challet, Marsili (2002)
- Challet, De Martino, Marsili (2004)
- Challet, De Martino, Marsili, Perez Castillo (2006)
Fat tails and volatility clustering
P(| A | x)  x
  2.8
for
ns  20

Problems
• Dependence on the
initial conditions
(non-ergodic
regime).
• Sample-to-sample
dependence.
• Finite-size effects.
GCMG with finite score memory
The payoff becomes
U i (t  1)  (1 

P
)U i (t ) 
Agents Memory is 
1


P
 (t )
ai
A(t ) 
time steps.
i
P
Reproducing Stylized Facts
• The dipendence on initial condition is removed.
• The disorder-sample dependence is removed.
*
• For    = 0.001 stylized facts are generated.
Multi-asset Minority Game
• Model with many assets:
The role of risk in choosing the asset: complex market structure.
- Bianconi, De Martino, Ferreira, Marsili (2006)
• Model with different information sources.
Can agent detect meaningful signals?
- De Martino, Tedeschi, Virasoro (in preparation)
Waiting times between orders and trades
• The data have been extracted from the ‘order book’ of the LSE.
•Our data set includes waiting times between orders and trades for both Glaxo Smith
Kline and Vodafone stocks traded in the months of March, June, and October 2002.
• Nearly 800,000 orders and 540,000 trades have been analyzed. Both limit and market
orders have been included.
•For orders and trades of each stock, the average waiting times and the standard
deviations are given in Table below. The difference between these two values already
points to a non-exponential distribution of durations.
-Scalas, Kaizoji, Kirchler, Huber, Tedeschi (2006)
Statistical Equilibrium in Economics
-Scalas, Gallegati, Guerci, Mas, Tedeschi (2006)
- Gallegati, Scalas and Tedeschi (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 H 
s j ln( s j )

j
Where for the theoretical quantities we consider:
 
)
and A  N (1  e
s j  Ae
 j
with
1
N
  ln( 1  )

S
Linear Dependency between volatility and activity
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
Absolute fluctuations vs.
time, and scatter-plot of
activity and volatility
Istogramma dei valori delle
correlazioni significative
(circa 70% del totale)