1. OCS
Econoﬁsica:
Alcuni tratti di una scienza ibrida
Rosario Nunzio Mantegna
Palermo University, Italy
Observatory of Complex Systems
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2. 2005
OCS
2009
Observatory of Complex Systems
http://ocs.unipa.it
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3. Outline
OCS
- Some changes affecting the society and science
- The modeling of economic complex systems with
concepts and methods from physics. Three examples:
1) the ﬁltering of information present in the
return dynamics of a stock portfolio;
2) the high frequency strategic action of economic
actors trading in a ﬁnancial market;
3) the empirical evidence of specialization of market
members acting in a ﬁnancial market.
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4. The IT revolution, Internet, the world wide web and its
structure (Google, Wikipedia, etc) have provided, produce
OCS
and allow access to an enormous amount of information.
From a project of Berkley University: http://www2.sims.berkley.edu
1,000,000,000,000,000,000 bytes —
10006, or 1018
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5. New approaches are pursued in the scientiﬁc practice and
in the social modeling:
OCS
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6. OCS
Changes in the scientiﬁc practice
Some disciplines which traditionally were characterized by
a low rate of production of scientiﬁc data have rapidly
moved to a status of disciplines producing a high rate
of data and information.
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7. Some disciplines which changed their status
OCS
For example biology, medical sciences and
social sciences have changed their status and today
they are characterized by a huge rate of production
of scientiﬁc data.
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8. OCS
From “The Economist” April 18th 2009
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9. In short we are entering in a new era of scientiﬁc practice
OCS
with a huge rate of scientiﬁc data production.
Cover of the special Nature issue of September 4th, 2008
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10. OCS
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11. It is however not only a matter of the size of the information
OCS
which is produced and available. The nature of data and the
associated data mining and data interpreting procedures raise
new challenges.
In most disciplines data produced are global and of
observational nature. This is quite different from what
was the standard in the XXth century when experimental
attention was localized and experiments where highly
controlled.
We therefore need new methodological approaches and new
techniques. Often the development of these new methods and
techniques emerges in an interdisciplinary (hybrid)
environment.
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13. OCS
H.A. Simon, Proc. of the American Philosophical Society 106, 467-482 (1962)
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14. Philip W. Anderson’s complexity manifesto
OCS
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15. A model complex system: The ﬁnancial market
OCS
Cross-correlation between pairs of stock
returns are well-known in financial markets
They may be quantified by
the correlation coefficient ρij
Ln P(t)
ri rj − ri rj
ρ ij =
2 2 2 2
ri − ri r − rj
j
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16. Grayscale representation of the correlation
OCS
matrix of a portfolio of stocks
n(n-1)/2
distinct
correlation
coefﬁcients
300 stocks
traded at the
US equity
markets in
2001-2003
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17. How to analyze the complexity of a
OCS
correlation matrix?
Clustering e.g.
Hierarchical Clustering
Super Paramagnetic Clustering
Maximum Likelihood Clustering
Sorting Point Into Neighbors
Random Matrix Theory
Correlation Based e.g. Minimum Spanning Tree (MST)
Networks Planar Maximally Filtered Graph (PMFG)
M. Tumminello, F. Lillo, R.N. Mantegna, Correlation, hierarchies, and networks in
ﬁnancial markets, Journal of Economic Bahavior & Organization (2010)
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19. Hierarchical clustering
OCS
AXP
MER
0.664
By starting from a correlation matrix
IBM
MER
0.617
(which is a similarity measure)
SLB
OXY
0.592
BAC
MER
0.591
AIG
IBM
BAC
AXP
MER
TXN
SLB
MOT
RD
OXY
RD
OXY
0.590
AIG
1
0.413
0.518
0.543
0.529
0.341
0.271
0.231
0.412
0.294
TXN
MOT
0.582
IBM
1
0.471
0.537
0.617
0.552
0.298
0.475
0.373
0.270
IBM
TXN
0.552
BAC
1
0.547
0.591
0.400
0.258
0.349
0.370
0.276
AXP
BAC
0.547
AXP
1
0.664
0.422
0.347
0.351
0.414
0.269
AIG
AXP
0.543
MER
1
0.533
0.344
0.462
0.440
0.318
AXP
IBM
0.537
TXN
1
0.305
0.582
0.355
0.245
SLB
RD
0.533
SLB
1
0.193
0.533
0.592
MER
TXN
0.533
MOT
1
0.258
0.166
AIG
MER
0.529
RD
1
0.590
AIG
BAC
0.518
OXY
1
IBM
MOT
0.475
MOT
MER
0.462
MER
RD
0.440
AXP
TXN
0.422
.......
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20. Hierarchical clustering
OCS
One may obtain a simpliﬁed matrix by using classical
clustering methods such us the single linkage clustering
AIG
IBM
BAC
AXP
MER
TXN
SLB
MOT
RD
OXY
AIG
1
0.543
0.543
0.543
0.543
0.543
0.440
0.543
0.440
0.440
IBM
1
0.591
0.617
0.617
0.552
0.440
0.552
0.440
0.440
BAC
1
0.591
0.591
0.552
0.440
0.552
0.440
0.440
AXP
1
0.664
0.552
0.440
0.552
0.440
0.440
MER
1
0.552
0.440
0.552
0.440
0.440
TXN
1
0.440
0.582
0.440
0.440
SLB
1
0.440
0.590
0.592
MOT
1
0.440
0.440
RD
1
0.590
OXY
1
C<SL
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21. Hierarchical clustering
OCS
Or, for example, the average linkage clustering
AIG
IBM
BAC
AXP
MER
TXN
SLB
MOT
RD
OXY
AIG
1
0.501
0.501
0.501
0.501
0.412
0.308
0.412
0.308
0.308
IBM
1
0.536
0.577
0.577
0.412
0.308
0.412
0.308
0.308
BAC
1
0.536
0.536
0.412
0.308
0.412
0.308
0.308
AXP
1
0.664
0.412
0.308
0.412
0.308
0.308
MER
1
0.412
0.308
0.412
0.308
0.308
TXN
1
0.308
0.582
0.308
0.308
SLB
1
0.308
0.562
0.591
MOT
1
0.308
0.308
RD
1
0.562
OXY
1
C<AL
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22. Hierarchical clustering output in a typical case
OCS
N = 100 (NYSE) daily returns 1995 -1998 C < = (ρ< )
ij
ρ < = ρα k
ij
€ where
αk
is the ﬁrst
€ node where
elements
€ i and j merge
together
Average Linkage Cluster Analysis
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23. OCS
Filtered matrix
N = 300 (NYSE); daily returns 2001- 2003
€
C < from ALCA C
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25. Correlation based networks
OCS
i
( i, j, ρij )
wij=ρij
j
1 3 0.90
1 0.13 0.90 0.81
1 4 081
0.13 1 0.57 0.34 3 4 0.71
C = → S =
0.90 0.57 1 0.71
2 3 0.57
0.81 0.34 0.71 1 2 4 0.34
1 2 0.13
Correlation Matrix (C)
Sorted List of Links (S)
†R.N. Mantegna, Eur. Phys. J. B 11, 193-197 (1999)
€
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26. Minimum Spanning Tree
OCS
Deﬁne a similarity measure between the elements of the system
Construct the list S by ordering similarities in decreasing order
Starting from the ﬁrst
element of S,
add the corresponding link
if and only if
the graph is still a Forest or a Tree
Minimum Spannig
Tree
(MST)
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27. Correlation based tree(s)
OCS
For the single
linkage clustering
procedure the
correlation based
tree is the minimum
spanning tree
Correlation based trees and hierarchical trees do
NOT carry the same amount of information.
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28. Minimum Spanning Tree
OCS
N=100 (NYSE)
daily returns
1995-1998
T=1011
G. Bonanno, F. Lillo and R.N.M., Quant. Fin. 1, 96 (2001)
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29. MST and Planar Maximally Filtered Graph
OCS
Deﬁne a similarity measure between the elements of the system
Construct the list S by ordering similarities in decreasing order
Starting from the ﬁrst
Starting from the ﬁrst
element of S,
element of S,
add the corresponding link
add the corresponding link
if and only if
if and only if
the graph is still a Forest or a Tree
the graph is still Planar (g=0)
Minimum Spannig Planar Maximally
Tree
Filtered Graph
MST
PMFG
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30. Planar Maximally Filtered Graph
OCS
N=100 (NYSE)
daily returns
1995-1998
T=1011
M. Tumminello, T. Di Matteo, T. Aste and R.N.M., PNAS USA 102, 10421 (2005)
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31. OCS
Network of crimes of a large set of
Swedish suspects
• Christofer Edling, (Jacobs University Bremen)
• Fredrik Liljeros (Stockholm, Sweden)
• Jerzy Sarnecki (Stockholm, Sweden)
• Michele Tumminello (Palermo)
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32. Sex offences
involving a
child
274 crimes
OCS
are in the
largest
Human
crime
trafﬁcking
community
and
procuring
Illegal
immigration
Misuse
of ofﬁce
Environmental
offences
Tax offences
Work environment act
A large network comprising 330 crimes with 14 530 links
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33. OCS
Price formation in a double auction ﬁnancial
market
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34. A detailed representation of book dynamics in a short
OCS
Price formation in a double auction market
period of time
- sell limit
AZN price (pence)
orders
- buy limit
orders
○ sell market
orders
x buy market
orders
time (s)
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35. Research challenges
OCS
Price formation and
liquidity disclosure
in platform based
competing markets.
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36. Price formation in a ﬁnancial market
OCS
Examples of databases:
Rebuild order book
Open book and TAQ
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37. We♩ have investigated the conditional spread decay
G(τ | Δ) and the relation between permanent ( I ) and
OCS
immediate ( Δmo) price impact
♩A.Ponzi, F. Lillo, R.N.Mantegna, Market reaction to a bid-ask spread change: A power-law relaxation
dynamics; PRE 80, 016112 (2009).
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38. The permanent impact is a fraction of the immediate
price impact
OCS
Data obtained by investigating 71 highly liquid stocks of the LSE
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39. The conditional spread decay is a power-law decay
suggesting the existence of a strategic placement
OCS
of limit and market orders
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40. Indeed the rate of orders arriving into the market
OCS
is a function of the value of the spread.
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41. Order placement also affects “time to ﬁll”♩
OCS
♩Z. Eisler, J. Kertesz, F. Lillo and R.N. Mantegna, Diffusive behavior and the modeling of
characteristic times in limit order executions, Quantitative Finance 9, 547 (2009).
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42. OCS
GSK
AZN
First passage time
LLOY
SHEL
λ ≈ −1.5 VOD
Time to ﬁll
λ ≈ −2
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€
44. Conceptual challenges
OCS
The most basic assumption of idealized systems
used in economic theory.
In mainstream economics, the economic actor is described in terms
of a representative agent, which is:
- fully rational;
- has access to all available information;
- is able to process all information instantly and without errors.
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45. Conceptual challenges
Equilibrium theory is a milestone of classic economic theory.
OCS
However it is a static description.
Steve Smale, Mathematical Problems for the Next Century,
August 7, 1998, Second Version
“ Problem 8: Introduction of dynamics into economic theory.
The following problem is not one of pure mathematics, but lies on the interface of
economics and mathematics. It has been solved only in quite limited situations.
Extend the mathematical model of general equilibrium theory to include price
adjustments. There is a (static) theory of equilibrium prices in economics starting
with Walras and ﬁrmly grounded in the work of Arrow and Debreu (see Debreu, 1959).
For the simplest case of one market this amounts to the equation supply equals
demand and a natural dynamics is easily found (Samuelson, 1971). For several markets,
the situation is complex. ............
Problem 8 asks for a dynamical model, whose states are price vectors (perhaps enlarged
to include other economic variables). This theory should be compatible with the existing
equilibrium theory. A most desirable feature is to have the time development of prices
determined by the individual actions of economic agents.
I worked on this problem for several years, feeling that it was the main problem of
economic theory (Smale, 1976). See also (Smale, 1981a) for background.”
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46. Conceptual challenges
Heterogeneity at the micro level
OCS
The Journal of Political Economy, Vol. 109, No. 4 (Aug., 2001), pp. 673-74
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47. An empirical analysis of heterogeneous trading
OCS
behavior: The Spanish stock market
Market members are credit entities and investment firms
which are members of the stock exchange and are entitled
to trade in the market.
Approx 200 market members at the BME (350/250 at the NYSE)
We only study approximately 80 because:
Not all the members trade during the whole period
We have only chosen those members whose activity is
continuous
Snapshot of our database
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48. Market members vs agents
OCS
Market members (MMs)
are not agents. A market
member may act on
behalf of many different
agents.
This could be due either
because a MM acts as an
intermediary or because
a MM is doing client
trading.
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49. Data
OCS
We investigate 4 highly capitalized stocks: Telefonica
(TEF), Banco Bilbao Vizcaya Argentaria (BBVA),
Banco Santander Central Hispano (SAN) and
Repsol (REP)
The investigated period is 2001-2004
We investigate market dynamics by focusing on the
trading of each selected stock separately for each
available calendar year.
By doing so we have up to 4x4 distinct sets of results
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50. Investigated variable
OCS
Inventory variation = the value (i.e. price times volume)
of an asset exchanged as a buyer minus the value exchanged as a
seller in a given time interval.
t +τ
v i ( t ) ≡ ∑εi ( s) pi ( s)Vi ( s)
s= t
sign
+1 for buys
price
volume
-1 for sells
In this talk, we investigate the τ = 1 trading day
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52. Correlation matrix of MM inventory variation
OCS
Is the cross correlation matrix of MM
inventory variation carrying information
about the market dynamics?
A random null hypotesis can be tested by
using Random Matrix Theory
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53. Eigenvalue spectrum
OCS
1st eigenvalue
Shufﬂing threshold
2nd eigenvalue
RMT threshold
The ﬁrst eigenvalue is not compatible with random trading and is
therefore carrying information about the collective dynamics of ﬁrms.
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54. Origin of collective behavior
OCS
• Which is the meaning of the largest eigenvalue of the correlation
matrix of inventory variation?
• Principal Factor Analysis suggests that there is a factor which is
driving the inventory variation of many ﬁrms
• The presence of the collective behavior is not due to the fact that
some ﬁrms are buying and other are selling (shufﬂing experiment)
• Rather it suggests that there are groups of ﬁrms having
systematically the same position in the market as the other
members of the group they belong to.
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55. The factor driving inventory variation is
OCS
signiﬁcantly correlated with price return
Correlation between the factor and price return ranges between
0.47 and 0.74, being statistically signiﬁcant at 99% conﬁdence in
all 16 sets
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56. A taxonomy of market members
OCS
Uncategorized
“noisy” ﬁrms
“trending” MMs
“reversing” MMs
(ex: momentum
(ex: contrarian
traders)
traders)
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57. A closer look on all ﬁrms in the 4x4 sets
OCS
variation with stock return
Correlation of inventory
Block bootstrap validation
Block bootstrap validation
Lillo, Moro, Vaglica and RNM, New Journal of Physics, 10 (2008) 043019
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58. BBVA 2003
OCS
Inventory variation R
correlation matrix
obtained by sorting
the MMs in the rows
and columns
according to their U
correlation of
inventory variation T
with price return
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59. OCS
The taxonomy is rather stable over the years
Categorization of active MMs for the Telefonica Stock
TEF 2001 2002 2003 2004
Reversing 43 39 42 37
Uncategorized 28 31 31 29
Trending 11 10 8 6
Total 82 80 81 72
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60. Specialization is stable over the years
OCS
P(Y|X) is the probability that a MM of the group X
switches to group Y in the next year (data for
Telefonica stock averaged over 3 years)
X
Reversing Uncategorized Trending
Reversing 0.71 0.19 0.03
Uncategorized 0.16 0.62 0.35
Y
Trending 0.02 0.07 0.44
Exited 0.11 0.12 0.18
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61. Conclusions
OCS
There is a growing role of the observational
approach in several scientiﬁc disciplines.
Economics and social sciences are among
the disciplines with a high rate of data
production.
In the modeling of ﬁnancial markets it is
essential to consider the intrinsic
heterogeneity of the economic actors.
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62. "The only hero able to cut off Medusa's
head is Perseus, who ﬂies with winged
OCS
sandals. ..... . To cut off Medusa's head
without being turned to stone, Perseus
supports himself on the very lightest of
things, the winds and the clouds, and
ﬁxes his gaze upon what can be revealed
only by indirect vision, an image caught
in a mirror. I am immediately tempted to
see this myth as an allegory on the poet's
relationship to the world, a lesson in the
method to follow when writing."
Michelangelo Merisi
da Caravaggio
Italo Calvino, Six Memos for the Next Millennium
Head of Medusa (1598)
Vintage Books, Random House, New York 1988
Ufﬁzi gallery
OCS website: http://ocs.unipa.it
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