Characteristics of Real Futures Trading Networks

Abstract

Futures trading is the core of futures business, and it is considered as one
of the typical complex systems. To investigate the complexity of futures
trading, we employ the analytical method of complex networks. First, we use
real trading records from the Shanghai Futures Exchange to construct futures
trading networks, in which nodes are trading participants, and two nodes have a
common edge if the two corresponding investors appear simultaneously in at
least one trading record as a purchaser and a seller respectively. Then, we
conduct a comprehensive statistical analysis on the constructed futures trading
networks. Empirical results show that the futures trading networks exhibit
features such as scale-free behavior with interesting odd-even-degree
divergence in low-degree regions, small-world effect, hierarchical
organization, power-law betweenness distribution, disassortative mixing, and
shrinkage of both the average path length and the diameter as network size
increases. To the best of our knowledge, this is the first work that uses real
data to study futures trading networks, and we argue that the research results
can shed light on the nature of real futures business.

Full text

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arXiv:1004.4402v1 [q-fin.ST] 26 Apr 2010
Characteristics of Real Futures Trading Networks
Junjie Wanga,b, Shuigeng Zhoua,c,∗
aSchool of Computer Science, Fudan University, Shanghai 200433, China
bShanghai Futures Exchange, Shanghai 200122, China
cShanghai Key Lab of Intelligent Information Processing, Fudan University, Shanghai 200433, China
Abstract
Futures trading is the core of futures business, and is considered as a typical complex system.
To investigate the complexity of futures trading, we employ the analytical method of complex
networks. First, we use real tradingrecordsfromShanghaiFutures Exchangeto constructfutures
trading networks, in which vertices are trading participants, and two vertices have a common
edge if the two corresponding investors simultaneously appear in at least one trading record as a
purchaser and a seller respectively. Then, we conduct a comprehensivestatistical analysis on the
constructedfuturestradingnetworks,andempiricalresultsshowthatthefuturestradingnetworks
exhibit such features as scale-free structure with interesting odd-even-degree divergence in low
degreeregion,small-worldeffect,hierarchicalorganization,power-lawbetweennessdistribution,
and shrinkage of both average path length and diameter as network size increases. To the best of
our knowledge, this is the first work that uses real data to study futures trading networks, and we
argue that the research results can shed light on the nature of real futures business.
Keywords: Complex networks, Futures trading networks, Scale-free scaling, Small-world effect
PACS: 89.75.Fb, 89.75.Hc, 89.65.Gh
1. Introduction
Since the works of Watts & Strogatz [1] and Barab´ asi & Alberta [2] were published, com-
plex networks, as a new scientific area, have caught a tremendous amount of interest [3–7].
Complex networks can describe a wide range of real-life systems in nature and society, and
show various non-trivial topological characteristics not occurring in simple networks such as
regular lattices and random networks. There are a number of frequently cited examples that
have been studied from the perspective of complex networks, including World Wide Web [8–
11], Internet [12], metabolic networks [13], scientific collaboration networks [14], online social
networks [15, 16], public transport networks [17, 18], airline flight networks [19] and human
language networks [20–22]. Empirical studies on these networks mentioned above have largely
motivated the recent curiosity and concernabout this new research area so that a numberof tech-
niques and models have been explored to improvepeople’s perception of topologyand evolution
of real complex systems [23–28]. As growing in importance and popularity, complex network
∗Corresponding address: School of Computer Science, Fudan University, 220 Handan Road, Shanghai 200433, China
Email addresses: wangjunjie@fudan.edu.cn (Junjie Wang), sgzhou@fudan.edu.cn (Shuigeng Zhou)
Preprint submitted to Physics AApril 27, 2010

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theory becomes a powerful tool with intuitive and effective representations to analyze complex
systems in a variety of fields, including financial market [29].
In the literature, a number of papers have been dedicated to studying financial market from
the perspective of complex networks. The major difference among these works lies in the types
of networks to be constructed from financial data for characterizing the organization and struc-
ture of financial market. Some existing works constructed stock networks whose connectivity is
defined by the correlation between any two time series of stock prices [30–34]. Some others es-
tablished directed networks of stock ownership describing the relationship between stockholders
and companies [35, 36]. Networks of market investors based on transaction interaction between
the investors were also investigated. For example, Franke et al analyzed irregular trading be-
haviors of users in an experimental stock market [37], while Wang et al studied the evolving
topology of such a network in an experimental futures exchange [38].
The study on financial investor networks can provide clues to reveal the true complexity in
financial market, especially futures market. In a real futures market, the futures trading model
serves as a matching engine to execute all eligible orders from various market participants, and
the interactions among the participants form a complex exchange network, which is termed as
futures trading network (FTN in short) in this paper. Simply, a FTN consists of a set of trading
participants, each of which has at least one connection of direct exchange action to another on
the futures contracts.
In this paper, we try to provide a comprehensivestudy on the characteristics of futures trading
networks established with genuine trading data from Shanghai Futures Exchange. To the best
of our knowledge, this is the first work that uses real futures trading data to construct networks.
So we think the empirical results may unveil the financial trading behavior and shed light on the
nature of futures market.
The rest of this paper is organized as follows. FTN construction method is introduced in
Section 2, including trading data set and the detail of network construction. Section 3 presents
the empirical results of FTNs. Section 4 concludes the paper.
2. Construction of Futures Trading Networks
In this section, we first introducethe real tradingdata fromShanghaiFutures Exchange,which
will be used to construct futures trading networks, and then present the detail of futures trading
networks construction.
2.1. Dataset
To construct futures trading networks, we use real trading records from Shanghai Futures
Exchange, which is the largest one in China’s domestic futures market and has considerable
impact onthe globalderivativemarket. Traderecordsaregeneratedby matchingordersor quotes
from buyers and sellers according to a certain rule of price/time priority (first price, then time)
in the electronic trading platform of the futures exchange. There are hundreds of thousands
of matching results reported from the exchange in one typical trading day. We use a dataset
involving all futures commodities in the derivative market from July to September of 2008. For
the trading records, we use virtual and unique IDs to represent the trading participants, and all
other information is filtered for privacy preservation reason.
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2.2. Network Construction
Since a trading record contains the IDs of both the buyer and the seller, we are able to es-
tablish a futures trading network. The construction process is as follows. A vertex represents
a participant in a trading record, and an edge, meaning a trade relation, is established between
two participants if their IDs appear in the same trading record at least once. An example of FTN
comprising nine records is shown as Fig. 1. Here, A-H are IDs of trading participants. Each row
in the right part of Fig. 1 represents a trading record, and the Seller and Buyer columns are the
IDs of seller and buyer in each trading record.
?????????????
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???????????
???????????
?
?
?
?
?
?
?
?
Fig. 1. An example of futures trading network constructed from a dataset with nine trading records.
Following the above process, we first create the largest network with the whole dataset con-
taining three months’ trading records, this network is denoted as FTN-all. Then, we construct
three sub-networks based on three subsets of the whole dataset above according to futures com-
modity classification of Shanghai Futures Exchange. These three sub-networks are termed as
FTN-met, FTN-rub and FTN-oil, which involve only futures commodity metal (concretely in-
cluding copper, aluminum, zinc and gold), natural rubber and fuel oil respectively. Thus, we
have totally four FTNs, their detailed information is given in Table 1.
Table 1. The details of the four FTNs. FTN-all is based on the whole dataset containing three months’
trading records from July to September of 2008, FTN-met, FTN-rub and FTN-oil are three sub-networks
of FTN-all, they correspond to three subsets that involve only trading records of futures commodity metal,
natural rubber and fuel oil respectively.
Label Futures Commodity
FTN-all
all
FTN-met
metal
FTN-rub
natural rubber
FTN-oil
fuel oil
Number of vertices
100994
75262
55828
52208
Number of edges
8068676
3226119
3364557
1657268
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3. Properties of Futures Trading Networks
In what follows, we study the characteristics of FTNs constructed above, our focus is on
topological features and dynamical properties. Extensive empirical results are presented.
3.1. Scale-free Behavior
Degree distribution P(k) is one of the most import statistical characteristics of a network, and
one of the simplest properties that can be measured directly, whose definition is the probability
that a random vertex in a network has exactly k edges. In many real complex networks, P(k)
decays with k in a power law, following P(k) ∼ k−λ. A network owning such a property is called
scale-free network [2].
The degree distributions of FTN-all, FTN-met, FTN-rub and FTN-oil are shown in
Fig. 2(a), (b), (c) and (d). We can see that the P(k) of all the four networks follows power-law
distribution with the same λ value, which is about 1.5. This implies that highly connected ver-
tices have larger chances of occurring and dominating the connectivity. Actually, these vertices
correspond to a few active speculators who send numerous orders to the exchange, and conse-
quently obtain more opportunities to make deals with the others. Their trading behaviors also
account for the fact that FTNs dynamically expand in accordance with the rule of preferential
attachment by continuously adding new vertices during the lifetime of the networks.
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Fig. 2. Degree distributions of FTN-all, FTN-met, FTN-rub and FTN-oil. All the four fitting lines in the
subplots have the same slope and follow P(k) ∼ k−1.5.
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In Fig. 2, we also can see the fact that in low-degree region, the probability of even degree is
larger than that of odd degree following the former, which forms a divergence. As the degree
increases, the two branches gradually converge and the difference is averaged out. The branch
of even degree conforms to power law more than that of the odd. For this observation, one
reasonable explanation is that most participants with a small number of trading transactions are
unwilling to hold the positions long term, which are open not long ago, and close them soon. To
a certain extent, due to the randomicity of counter part during the execution, two matches (open
and close) of a participant are more possible to be involved in different counter parties, thus two
degrees will be added to the corresponding vertex. This observation reveals that there are few
hedgers with long-term position in real trading, which is consistent with the fact of low delivery
ratio in the futures market.
Now let us consider weighted futures trading networks where vertex strength is a significant
measure [39]. In this paper, the vertex strength is defined as follows. Suppose that the weight of
an edge between two vertices is the number of times they appear in the same trade record, the
strength S of a vertex is defined as the total weight of all edges connecting it. As shown in Fig. 3,
the relationship between the strength and degree of all vertices in FTN-all shows a nontrivial
power law scaling S ∼ kβ, which demonstrates the fact that active market participants get more
active. Such a scale-free behavior being correlated to the occurrence frequency of a trading
participant provides another justification for the power-law degree distribution of the networks.
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Fig. 3. Plot of the vertex strength S as a function of degree k in FTN-all, the slope is about 1.18.
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3.2. Small-world Effect
For complex networks, average path length and clustering coefficient are two important mea-
sures of small-world effect.
In a network, the average path length (say L) is defined as the number of edges in the shortest
path between any two vertices, averaged over all pairs of vertices. It plays an important role in
transportation and communication in a network. We can obtain L = (2/n(n − 1))?
longest shortest path among all pairs of vertices is called the diameter of the network.
The clustering coefficient Ciof a vertex i is defined as the ratio of the total number eiof edges
that actually exist between all its kiimmediate (nearest) neighbors and the number ki(ki− 1)/2
of all possible edges between them, that is, Ci= 2ei/ki(ki− 1). The clustering coefficient C of
the whole network is the average of Ciover all vertices, i.e., C = (1/n)?Ci. The clustering
coefficient measures the probability that two neighbors of a vertex are connected and reveals the
local cliquishness of a typical neighborhoodwithin a network.
In recent empirical studies, many real systems show small-world effect by two crucial factors:
average path length and diameter is relatively small despite often the large network size, which
grows nearly logarithmically with the number of vertices, and the clustering coefficient is larger
than that of a comparable random network having the same number of vertices and edges as the
real network.
We also notice small-world effect in FTN-all. On one hand, the average path length L and
diameter D are small, their values are 2.470 and 6 respectively, while the values are 2.774 and 4
in an equivalent random network with the same parameters. On the other hand, the network is
highly clustered. The clustering coefficient of FTN-all is 0.0480, which is larger than that of the
random network (the value is 0.0016). These results are presented in Table 2.
i≥jdij. The
Table 2. Small-world effect shows in FTN-all with large clustering coefficient C and small average path
length L and diameter D, contrary to a random network with similar parameters (total number of vertices V,
total number of edges E or average number of edges per vertex < k >)
Label
VE
< k >
FTN-all
1009948068676159.8
random
---
kmax
36878
218
CLD
6
4
0.0480
0.0016
2.470
2.774
The ratio of CFTN−alland Crandis relatively small in comparison with other real systems [4].
This implies no adequate evidence of local cliquishness of a typical neighborhood within FTN-
all, which may be due to the randomicity of counter part during execution. Furthermore, the
small L and D is because of 1) the existence of hub vertices (conforming to the large maximum
degree kmaxin Table 2), which are bridges between different vertices separated in the network;
and 2) new connections generated between the existing vertices without direct links previously,
which provide more shortcuts to the network. The shortest path distribution in Fig. 4 shows that
most of the shortest paths are 2 or 3, which helps to explain the small-world effect.
3.3. Hierarchical Organization
To examine the hierarchical organization feature of a network, we check C(k), the average
clustering coefficient of all vertices with the same degree k. If C(k) follows a strict scaling law,
the network is viewed as the presence of hierarchical organization. Some real networks, such as
World Wide Web, actor network and Internet, display the hierarchical topology [40].
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123456
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Fig. 4. Shortest path distribution indicating that most of the shortest paths are 2 or 3.
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For FTN-all, as indicated in Fig. 5, the main part of C(k) obeys a scaling law of k−0.8, which
implies that the network has a hierarchical architecture. Although the majority of bargainers
making a few deals have a few links (low k), most of these links join hub vertices that connect
to each other, resulting in a big C(k). The high-k vertices are hub bargainers,and their neighbors
being low-k vertices are seldom linked to each other, leading to a smaller C(k). This implies
that ordinary investors are part of such clusters with high cohesiveness and dense interlinking
except the hubs that play a bridging role to connect many separate small communities together
into a complete network. To some extent, the hub investors flourish the market and improve the
market’s liquidity.
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Fig. 5. Clustering coefficient C(k) as a function of the vertex degree k with a exponent of -0.80
3.4. Betweenness Distribution
Betweenness is a measure of the centrality of a vertex in a network, and also a measure of the
influence a vertex has over the spread of information through the network [41].
The betweenness of a vertex is defined to be the fraction of shortest paths between pairs of
vertices in a network that go through it. If there is more than one shortest path between two
vertices, the value of each such path is weighted by one over the number of shortest paths. To
be precise, the definition is as follows: b(i) =?bjk(i)/bjkwhere bjk(i) is the number of geodesic
paths from j to k containing i, while bjkis the total number of geodesic paths linking j and k.
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By exploring the betweenness distribution P(b) of FTN-all, we find it following a power law
function, i.e., P(b) ∼ b−ωwith ω=0.8. The result is illustrated in Fig. 6.
Information communication (e.g. money or asset transfer) exists in FTNs, and money flow
is considered as the index of marke. The power-law distribution demonstrates that the vertices
havinghighbetweennessownsuchapotentialtocontrolinformationflowpassingbetweenvertex
pairsofthenetwork. Accordingly,theparticipantswithhighbetweennesscentralityplaydecisive
role in promoting market boom and enhancing financial function.
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Fig. 6. Betweenness distribution following a power law function with P(b) ∼ b−0.8
3.5. Power-Law Evolution
We have now explored topological properties in static FTNs. Here we will check some dy-
namic characteristics of the FTN-all network by considering its evolutional process, which can
characterize the real trading behaviors of futures market.
Like many real-life systems [10, 12, 13], FTN-all also shows accelerated growth [42]
in Fig. 7(a), which manifests that the number of edges increases faster than the number of ver-
tices. Furthermore, the relationship between the number of edges and the number of vertices in
FTN-all follows a power law function e(t) ∼ v(t)α, where e(t) and v(t) respectively denote the
numbers of edges and vertices of the network at time t, and α is the exponent. Such relationship
is termed densification power law by Leskoverc et al. [43]. We can see that the fitting curve
in Fig. 7(a) consists of two segments with different slopes, 1.8 and 3.3 respectively. We notice
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that the critical point of the broken fitting line exactly locates at the end of the first trading day,
meaning that the mechanism of intraday edge’s growth in FTN-all is totally different from that
after the first day.
Besides, we observe that the average degree and density of FTN-all super-linearly grow with
the network size, and both show broken lines in the logarithmicplots of Fig. 7(b) and (c), similar
to Fig. 7(a). The variations of both average degree and density over time are directly related to
the change of edges’ number. The average degree¯k(t) and density d(t) are respectively evaluated
by¯k(t) = 2e(t)/v(t) and d(t) = 2e(t)/v(t)(v(t) − 1), and thus we obtain¯k(t) ∼ v(t)α−1and d(t) ∼
v(t)α−2. In Fig. 7(b),thetwoslopesofthebrokenlineare0.8and2.3respectively,andinFig. 7(c)
they are -0.2 and 1.3 respectively, which explains why the broken line of the density first falls
and then rises. According to Fig. 7(a), (b) and (c), FTN-all is becoming denser as the network
size increases.
InFig. 7(d),themaximumdegreekmax(t)ofFTN-allgrowsinpowerlaw: kmax(t) ∼ v(t)βwhere
the slope β is 1.7. This observation illustrates that the active participants in the futures market
keep vigorous all the time, and the day traders (these who frequently buy and sell futures within
the same trading day so that all positions will customarily be closed before the market close’s on
that day) constitute the core part of the active participants.
In some real complex networks [1, 9], the average path length scales logarithmically with the
number of vertices, and the diameter slowly grows with network size. However, in FTN-all we
notice that the average path length deceases as the number of vertices increases, so does the
diameter. The average path length decays in a power law with a slope of -0.27 in Fig. 7(e),
while the diameter of FTN-all deceases as shown in Fig. 7(f). With the network size’s growing,
the simultaneous shrinkage of both the average path length and the diameter in FTN-all provides
another evidence of densification in the network.
The exposed properties above indicate that the vertices in FTN-all become closer with each
other as the network size grows. These properties attribute to the real trading behavior of futures
market. The deals are resulted from two sources: trading of new investors who just enter the
market, and transactions between the existing participants. The new investors make a few deals
because of caution and carefulness, while the existing participants, especially the day traders,
generate a large number of transactions. The latter provide many chances to make deals between
the participants without any trading relationship before, which results in the new links between
the vertices that have no direct connectionspreviouslyin FTN-all, and consequentlyaccounts for
the properties mentioned above. Additionally, the different dominant sources of edge addition
determine the discontiguous slopes in the logarithmic plots. In the first trading day, almost all
investors are newcomers, so the edge growth from new investors is the dominant factor. After
that day, the number of new investors and their transactions tend to remain steady, and the edges
generatedbetweenthe existingparticipantsoutnumberthosegeneratedbythe new investors. The
conversion of the edge growth’s driving factors explains the existence of two different exponents
in the power law underlying the network’s evolution.
4. Conclusion
Futures trade networks in financial business have been analyzed from the perspective of com-
plex network. We constructed FTNs by using real trading records covering three months’ op-
eration in Shanghai Futures Exchange. We found a number of interesting statistical properties
of the networks, including scale-free behavior, small-world effect, hierarchical organization and
power-law evolution characteristics. Some unique features of the FTNs are possibly due to the
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Fig. 7. (a) The number of edges vs. the number of vertices in log-log scale for FTN-all, a power law is
witnessed with the slopes of 1.8 and 3.3 respectively in the evolution process. The critical point locates
at the end of the first trading day. (b) Average degree super-linearly grows in a power law with the slopes
of 0.8 and 2.3 respectively. (c) Density changes over time in an approximate power law of the slopes -0.2
and 1.3, and the slope values account for the reason why the curve first falls and then rises. The conversion
of edge growth’s driving factors results in the different slopes in the power law underlying the network’s
evolution. (d) Maximum degree grows in a power law with regard to network size, and the slope is 1.7. (e)
Average path length decays in a power law with a slope of -0.27. (f) Diameter decreases as the number of
vertices increases.
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randomicityof counterpart duringdeal executionand the continuousgenerationof new links be-
tween previously-unconnectedvertices, which play important roles in determining the structures
of futures trade networks.
As only undirected graphs are considered in this paper, it is worthy of further studying the
directedFTNs basedon tradingdirection,suchas frombuyerto seller, whichreflects information
flow, for example, money flow. In Section 3.1, we simply established the weighted FTN-all
to demonstrate that active market participants get more active, but it is obviously not enough.
Actually, we can construct weighted FTNs or weighted and directed FTNs to investigate the
market behavior of active parts. Moreover, the generation model of FTNs is also an important
issue for further exploration, as it can provide valuable insight on financial trade monitoring and
risk control.
Acknowledgements
We thank Prof. Yunfa Hu and Zhongzhi Zhang for their valuable comments and suggestions.
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