rosario nunzio mantegna - lorentz center talk... · statistically validated networks of market...

Statistically validated networks of market members trading at the LSE electronic and

dealers' market

Rosario Nunzio Mantegna Central European University, Budapest, Hungary

Palermo University, Palermo, Italy

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Outline

28 May, 2013 Lorentz Center

-  I present results investigating the trading behavior of market members of a major stock exchange, the London Stock Exchange.

-  I discuss a methodology able to detect preferential relationships among market members in the (anonymous) electronic and (transparent) dealers' (off-book) venues of the market - I will discuss an important aspect of economic and social complex systems: the fundamental difference between anonymous and networked markets. - I will also discuss aspects of another networked market: the credit market for large firms in Japan.

28 May, 2013 Lorentz Center 3 3 3

LSE work is done in collaboration with

Michele Tumminello Fabrizio Lillo

Gabriella Vaglica Angelo Carollo

4

Our study is performed by investigating the trading action of market members of London Stock

Exchange Market members (MMs) are not single investors. In fact, a market member may act on behalf of many different investors.

A MM may act as an

intermediary and/or can do client trading and/or

proprietary trading. 28 May, 2013 Lorentz Center

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At LSE there are two different market venues Market members (MMs) can execute their trades by

submitting their orders in the electronic book in an anonymous form or can execute transaction in the

dealers' off-book venue by directly interacting with other (known) MMs. Recorded transactions are anonymous in both cases. Also some non Members are allowed to trade in the off-book venue of the market.


Electronic book

Off-book venue

MM

n MM

MM MM MM

MM MM MM MM

MM MM

28 May, 2013 Lorentz Center 6

Anonymous trading

Bilateral trading


We have access to a version of the Rebuild Order Book of the London Stock Exchange with anonymized identity of the Market Members for the years 2004-2006. The data include electronic transactions and off-book transactions. For the same period we also have access to the data of the Spanish Stock Market (BME) that are transparent to the identity of the Market member when the transaction is performed. However, in the case of the BME the off-book market present only a limited number of large (in volume) transactions.


Summary stastistics for 2004, in Angelo Carollo, Gabriella Vaglica, Fabrizio Lillo and Rosario N. Mantegna, Trading activity and price impact in parallel markets: SETS vs. off-book market at the London Stock Exchange, Quantitative Finance, Vol. 12, No. 4, April 2012, 517–530


Are trades occurring among market members showing a deviation from a null hypothesis of random pairing?

We investigate the preferential trading of MMs trading 5 highly liquid stocks (BP, HSBA, LLOY, RBS, and VOD) in both market venues during2005. The study is performed by using the transaction and order book records of the LSE having information about the (coded) identity of market members.

A key problem of this analysis is to properly take into account the heterogeneity in the trading profile of different MMs.


The case of Market Members trading BP during 2005 Transactions Volume Transactions VolumeOff1book Off1book On1book On1book

Mean 523.1 3.26E+07 7942.8 8.37E+07min 0.0 0.00E+00 0.0 0.00E+00max 28304.0 8.33E+08 198338.0 1.70E+09std 2316.3 1.06E+08 26538.7 2.72E+08

Nt

Off-book

Pdf

28 May, 2013 Lorentz Center 11 11

Over-expression of the number of tradings observed between two market members in a given venue

Market member i is acting as a buyer in Nib transactions

Market member j is acting as a seller in Njs transactions

During the selected time period and in the considered venue the two market members did Nijbs transactions between them and all market members did Nt transactions

Suppose there are Nt transaction records in the investigated set. Suppose we are interested to compare the occurrence of two given states B and S of two market members MMi and MMj. Market member MMi is buying Nib times whereas market member MMj is selling Njs times. Let us call Nijbs the buy-sell transaction between them


A statistical validation

What is the probability that the Nijbs B-S transactions occurs by chance?

Nt

Total # of transactions

Njs Nib

Nijbs

# of buying transactions of MMi

# of selling transactions

of MMj

# of B-S transactions

between the two MMs

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A statistical validation is possible The probability of having exactly Nijbs B-S transactions between MMi and MMj is given by the Hypergeometric distribution

Hypergeometric distribution:

P(Nijbs | Nt,Nib,N js ) =

Nib

Nijbs

!

"

##

$

%

&&

Nt − Nib

N js − Nijbs

!

"

##

$

%

&&

Nt

N js

!

"

##

$

%

&&

p =1−i=0

Nijbs−1

∑

Nib

i

#

$%%

&

'((

Nt − Nib

N js − i

#

$

%%

&

'

((

Nt

N js

#

$

%%

&

'

((

p-value associated to a detection of a number of transactions Nijbs≥ X:

X = x P(x | Nt,Nib,N js )∑Expected number of buy-sell transactions under a random null hypotesis:

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28 May, 2013 Lorentz Center 14 April 19, 2011 14 Swissquote & EPFL day on quantitative finance Tumminello M, Miccichè S, Lillo F, Piilo J, Mantegna RN (2011) Statistically Validated Networks in Bipartite Complex Systems. PLoS ONE 6(3): e17994. doi:10.1371/journal.pone.0017994

Statistically validated networks

28 May, 2013 Lorentz Center 15 15

Our statistical validation is done by performing a multiple testing hypothesis and therefore we need a multiple hypothesis test correction.

We address the statistically validated network obtained with the Bonferroni correction as the Bonferroni network

Another less restrictive multiple hypothesis test correction is the False Discovery Rate (FDR) correction.

The most restrictive multiple hypothesis test correction is the so-called: Bonferroni correction. It is defined as follow: by requiring a θ statistical threshold for the single test, the threshold B for the multiple test procedure is set to B=θ/T where T is the total number of tested hypotheses.


Daily analysis: 252 trading days of 2005

market members

Fraction of links validated in two consecutive days

Statistical threshold θ=0.01


Daily scale El

ectro

nic

book

Original Bonferroni D

eale

rs' m

arke

t

seller buyer

Black arrows are validated links (at the Bonferroni level)


Weekly scale El

ectro

nic

book


eale

rs' m

arke

t


Monthly scale El

ectro

nic

book


eale

rs' m

arke

t


Whole period El

ectro

nic

book


eale

rs' m

arke

t


Daily scale


Weekly scale


The dealers' market is a networked market whereas the anonymous electronic market presents only a limited amont of statistical validations of preferential trading relationships.

This conclusion is supported by the fact that persistence of the statistically validated trading relationship is observed only in the dealers' market whereas in the electronic market the identity of validated links is strongly fluctuating over time.

We measure the persistence of specific links present in trading network by computing the mutual information of links as defined in D-M Song, M. Tumminello, W.-X. Zhou, and R. N. Mantegna, Evolution of worldwide stock markets, correlation structure, and correlation-based graphs, Phys. Rev. E 84, 026108 (2011)


original network

Bonferroni network


We can compare the Off-book book price with the On-book price present at the moment of the transaction


Approximately 95% of the Off-book transactions occurs within the spread or at the best bid or best ask

Occurrence of the Z=(P-bid)/(ask-bid) for the BP stock traded Off-book by LSE market members during May 2005


By using this information we can infer from the combined On-book Off-book data who is the initiator of the Off-book transaction

best bid best ask

Seller initiated

Buyer initiated In analogy with the Lee and Ready algorithm


Another networked market: the credit market for large Japanese firms.

Work done in collaboration with: L. Marotta, S. Miccichè, Y. Fujiwara, H. Iyetomi, H. Aoyama, and M. Gallegati

Banks

Large firms


We have partitioned the bipartite credit network in communities (clusters) by using a clustering algorithm working directly on the bipartite graph and using a modularity measure adapted to bipartite graphs¶

¶ M.J. Barber, Modularity and community detection in bipartite networks, Phys. Rev. E76, 066102 (2007).

Our dataset is based on a survey of firms quoted in the Japanese stock exchange markets (Tokyo, Osaka, Nagoya). The data were compiled from the firms' financial statements and survey by Nikkei Media Marketing, Inc. in Tokyo. They include the information about each firm's borrowing obtained from financial institutions; the amounts of borrowing and their classification into short-term and long-term borrowings based on 1-year contracts. We examined the period from the years 1980 to 2012 (more than three decades).


The number of clusters is increasing over the years


1980 2011

bank or firm label bank or firm label

bank

or fi

rm la

bel

bank

or fi

rm la

bel


Each bank is characterized by a specific attribute: - City banks - Regional banks - Life insurance banks - insurance banks - ...... - etc

Each firm is characterized by economic sectors and subsectors: - Electric and electronic equipment - Services - Wholesale trade - Real estate - ...... - etc

Statistical validation of over-expression of attributes

July 24, 2010 34 Unwinding Complexity - Port Douglas - Australia

For a given set of elements we count how many of some selected attributes are present in our complete set. We count the same information also inside each subset of interest. For the sake of simplicity, let us focus on a specific attribute (say bank classification) but a similar conclusion applies for different attributes. For each subset a and for each bank classification k we have the number Na,k of banks of type k present in the subset a, the number Na is the number of elements of subset a, Nk is the number of banks of type k in the subset and the number Nn is the number of banks in the complete set. The probability that X elements of subset a belongs to bank type k under a random null hypothesis is again given by the hypergeometric distribution H(X|Nn,Na,Nk) and a p-value can therefore be associated to the observation of Na,k occurrence.

Again this is a multiple hypothesis test procedure and a Bonferroni threshold is set as 0.01/Nch for each test of each cluster, where Nch is the number of characterizing aspects that are tested. In the example the number of different bank types.


We investigate the evolution over the years of the over-expression of attributes characterizing the clusters of banks and firms

We investigate as attributes: -) the classification of banks; -) the geographical location of firms; -) the economic sectors of firms.

The evolution over time of the largest cluster


Another large cluster


A smaller and more limited example

N

Total # of elements in the two years

K M X

# of elements of cluster A

# of elements of cluster B

# of co-occurrence of elements A and B

Communities flow − years 1988 − 1989

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

●

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10


Similarly to what done by Musmeci et al we validate the presence of a directed link between a cluster at year t and a cluster at year t+1 by using again the hypergeometric distribution Each node is a cluster obtained in a given year. Arrow indicates validation of the assumption that elements in common at years t and t+1 are over-expressed with respect to a random null hypothesis

1988 1989

€

p =1−i= 0

X −1

∑

Mi

$

% &

'

( ) N −MK − i

$

% &

'

( )

NK$

% & '

( )


We believe the above results provide evidence that the credit market is a networked market where attributes like the nature of the bank, its localization, and the nature of the firm, its localization and its economic sectors play an important role in determining the probability that a credit relationships will be agreed between a firm and a bank.


The raise of the shadow banking system in Japan?

409997 Code "Unknown" in the database

Commercial/Non−commercial credit ratios

Year

cred

it ra

tio

1980 1985 1990 1995 2000 2005 2010

0.0

0.2

0.4

0.6

0.8 Commercial credit ratio

Non−commercial credit ratio

Credit from Other non financial Institutions

Year

Tota

l cre

dit

1980 1985 1990 1995 2000 2005 20100e

+00

1e+0

72e

+07

3e+0

74e

+07

409995409996409997409997−long409997−short409998

Year

Year

Tota

l cre

dit

Cred

it ra

tio


1992 1993 1994 1995

1996 1997 1998 1999

2000 2001 2002 2003

Connections of the 409997 code "Unknown" in the database

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Conclusions


�  Network preferential trading relationships are present in the off-book venue of the LSE.

�  Network preferential relationships can be detected with a method based on the statistical validation against a null hypothesis taking into account heterogeneity of market members.

�  Network preferential relationships are also observed in the credit market.

rosario nunzio mantegna - lorentz center talk... · statistically validated networks of market...

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