Econofisica: alcuni tratti di una scienza ibrida

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Dipartimento di Fisica
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25 febbraio 2010

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Econofisica: alcuni tratti di una scienza ibrida

  1. 1. OCS Econofisica: Alcuni tratti di una scienza ibrida Rosario Nunzio Mantegna Palermo University, Italy Observatory of Complex Systems 25/2/2010 Dip. Fisica - Perugia 1
  2. 2. 2005 OCS 2009 Observatory of Complex Systems http://ocs.unipa.it 25/2/2010 Dip. Fisica - Perugia 2
  3. 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. 25/2/2010 Dip. Fisica - Perugia 3
  4. 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 25/2/2010 Dip. Fisica - Perugia 4
  5. 5. New approaches are pursued in the scientific practice and in the social modeling: OCS 25/2/2010 Dip. Fisica - Perugia 5
  6. 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. 25/2/2010 Dip. Fisica - Perugia 6
  7. 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. 25/2/2010 Dip. Fisica - Perugia 7
  8. 8. OCS From “The Economist” April 18th 2009 25/2/2010 Dip. Fisica - Perugia 8
  9. 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 25/2/2010 Dip. Fisica - Perugia 9
  10. 10. OCS 25/2/2010 Dip. Fisica - Perugia 10
  11. 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. 25/2/2010 Dip. Fisica - Perugia 11
  12. 12. OCS Hierarchically organized complex systems 25/2/2010 Dip. Fisica - Perugia 12
  13. 13. OCS H.A. Simon, Proc. of the American Philosophical Society 106, 467-482 (1962) 25/2/2010 Dip. Fisica - Perugia 13
  14. 14. Philip W. Anderson’s complexity manifesto OCS 25/2/2010 Dip. Fisica - Perugia 14
  15. 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 25/2/2010 Dip. Fisica - Perugia 15
  16. 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 25/2/2010 Dip. Fisica - Perugia 16
  17. 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) 25/2/2010 Dip. Fisica - Perugia 17
  18. 18. OCS Hierarchical clustering 25/2/2010 Dip. Fisica - Perugia 18
  19. 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 ....... 25/2/2010 Dip. Fisica - Perugia 19
  20. 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 25/2/2010 Dip. Fisica - Perugia 20
  21. 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 25/2/2010 Dip. Fisica - Perugia 21
  22. 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 25/2/2010 Dip. Fisica - Perugia 22
  23. 23. OCS Filtered matrix N = 300 (NYSE); daily returns 2001- 2003 € C < from ALCA C 25/2/2010 Dip. Fisica - Perugia 23
  24. 24. OCS Correlation based networks 25/2/2010 Dip. Fisica - Perugia 24
  25. 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) € 25/2/2010 Dip. Fisica - Perugia 25
  26. 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) 25/2/2010 Dip. Fisica - Perugia 26
  27. 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. 25/2/2010 Dip. Fisica - Perugia 27
  28. 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) 25/2/2010 Dip. Fisica - Perugia 28
  29. 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 25/2/2010 Dip. Fisica - Perugia 29
  30. 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) 25/2/2010 Dip. Fisica - Perugia 30
  31. 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) 25/2/2010 Dip. Fisica - Perugia 31
  32. 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 25/2/2010 Dip. Fisica - Perugia 32
  33. 33. OCS Price formation in a double auction financial market 25/2/2010 Dip. Fisica - Perugia 33
  34. 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) 25/2/2010 Dip. Fisica - Perugia 34
  35. 35. Research challenges OCS Price formation and liquidity disclosure in platform based competing markets. 25/2/2010 Dip. Fisica - Perugia 35
  36. 36. Price formation in a financial market OCS Examples of databases: Rebuild order book Open book and TAQ 25/2/2010 Dip. Fisica - Perugia 36
  37. 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). 25/2/2010 Dip. Fisica - Perugia 37
  38. 38. The permanent impact is a fraction of the immediate price impact OCS Data obtained by investigating 71 highly liquid stocks of the LSE 25/2/2010 Dip. Fisica - Perugia 38
  39. 39. The conditional spread decay is a power-law decay suggesting the existence of a strategic placement OCS of limit and market orders 25/2/2010 Dip. Fisica - Perugia 39
  40. 40. Indeed the rate of orders arriving into the market OCS is a function of the value of the spread. 25/2/2010 Dip. Fisica - Perugia 40
  41. 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). 25/2/2010 Dip. Fisica - Perugia 41
  42. 42. OCS GSK AZN First passage time LLOY SHEL λ ≈ −1.5 VOD Time to fill λ ≈ −2 25/2/2010 Dip. Fisica - Perugia 42 €
  43. 43. OCS Empirically detected resulting strategies 25/2/2010 Dip. Fisica - Perugia 43
  44. 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. 25/2/2010 Dip. Fisica - Perugia 44
  45. 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.” 25/2/2010 Dip. Fisica - Perugia 45
  46. 46. Conceptual challenges Heterogeneity at the micro level OCS The Journal of Political Economy, Vol. 109, No. 4 (Aug., 2001), pp. 673-74 25/2/2010 Dip. Fisica - Perugia 46
  47. 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 25/2/2010 Dip. Fisica - Perugia 47
  48. 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. 25/2/2010 Dip. Fisica - Perugia 48
  49. 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 25/2/2010 Dip. Fisica - Perugia 49
  50. 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 € 25/2/2010 Dip. Fisica - Perugia 50
  51. 51. OCS Correlation between MMs’ inventory variation min=-0.53 max=0.75 25/2/2010 Dip. Fisica - Perugia 51
  52. 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 25/2/2010 Dip. Fisica - Perugia 52
  53. 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. 25/2/2010 Dip. Fisica - Perugia 53
  54. 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. 25/2/2010 Dip. Fisica - Perugia 54
  55. 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 25/2/2010 Dip. Fisica - Perugia 55
  56. 56. A taxonomy of market members OCS Uncategorized “noisy” firms “trending” MMs “reversing” MMs (ex: momentum (ex: contrarian traders) traders) 25/2/2010 Dip. Fisica - Perugia 56
  57. 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 25/2/2010 Dip. Fisica - Perugia 57
  58. 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 25/2/2010 Dip. Fisica - Perugia 58
  59. 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 25/2/2010 Dip. Fisica - Perugia 59
  60. 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 25/2/2010 Dip. Fisica - Perugia 60
  61. 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. 25/2/2010 Dip. Fisica - Perugia 61
  62. 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 25/2/2010 Dip. Fisica - Perugia 62

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