dynamics of the fx market: a minimal spanning tree approach omer suleman occf and department of...
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Dynamics of the FX Market:A Minimal Spanning Tree Approach
Omer SulemanOCCF and Department of Physics
University of Oxford
Collaborators: N F Johnson, M McDonald, S Williams, S Howison
NetworksWorld Wide Web Yeast Proteins
High School Dating Stock Market
Networks
Fully Connected Network
Cyclic Network Tree: Acyclic Network
Networks of Financial Time Series Correlation Based Networks
Entities generating financial time series (stocks, indices, hedge funds or currencies) are represented by nodes.
Weighted edges between nodes represent the correlation between the time series generated by these entities.
this gives us a fully connected network with
½[n(n-1)] edges where n is the number of nodes.
Filtering the Connections
The fully connected network contains too many connections, each with a range of possible weights, and hence too much information for it to be useful.
A filter has to be applied to this network in order to extract the most important links between the nodes thus clustering them.
Any scheme to do this will need a measure of distance or dissimilarity between nodes.
Distance
The weights of the links between nodes are based on the correlation between them.
The most intuitive measure of distance is the Euclidian distance between the time series:
This is a non-linear transformation of the correlation which gives a metric distance between nodes.
Ultrametricity
Metric Space: d(x,x) = 0 d(x,y) = d(y,x) d(x,z) ≤ d(x,y) + d(y,z)
Ultrametric Space: u(x,x) = 0 u(x,y) = u(y,x) u(x,z) ≤ max{ u(x,y) , u(y,z) }
Ultrametric distance is a measure of distance found useful for data classification.
Many different Ultrametrics are possible on a space Out of all Ultrametrics such that: u(x,y) ≤ d(x,y)
the greatest is called the Subdominant Ultrametric which is unique and can be determined by a Minimal Spanning Tree.
Minimal Spanning Tree
Tree: A connected graph without cycles is called a tree.
Spanning Tree: A subgraph that is a tree and reaches out to all vertices of the original graph is called a spanning tree of the graph.
Minimal Spanning Tree: Out of all possible spanning trees of a graph the one with minimum total edge weight is called the Minimal Spanning Tree of the graph.
MST in Finance – Equity Market
Mantegna, J-P Onnela et. al.
MST in Finance – Hedge Funds
Miceli and Susinno
MST and FX Market
Hedge fund profits and stock market returns can be measured in a single currency.
Nothing in the currency market is absolute. Prices for a currency are quoted relative to
another, usually USD. How do we build the tree without missing out
any currency?
Data Description
We look at XAU and 10 currencies USD, CAD, GBP, DEM, CHF, SEK, NOK, AUD, NZD and JPY from Jan 1993 to Dec 1994.
Thus we have hourly data points for 10 time series of the form USD/X.
We expand this set to all time series Xi/Xj possible in this group.
This gives us 110 different time series, with every currency represented in the network.
Trees of Hourly Data
Gold Cluster
AUD Cluster
Spurious Correlations? Triangle Effect
Correlation of returns:
Comparison of Real and Random Trees
Currency MST for 1993-94 Intersection of real and random MST for 1993-94
Degree Distributions
Dynamic MSTs
Stability of MST
0 500400300200100
1.00
0.82
0.90
dt
Single step survival ratio
Multi-step Survival of Links
1.0
0
5000 1000 1500 2000 2500 3000 4000 4500
Dynamics of JPY Cluster
Clustering Coefficient and Dynamics
JPY Clustering Coefficient
0
50
100
150
200
250
300
350
400
1 12 23 34 45 56 67 78 89 100 111 122 133 144 155 166 177 188 199 210 221 232
JPY
Work in progress
We are currently applying this analysis to higher frequency data (5 min, tick data). We hope this will give us a real time picture of the market and indicate the currencies “in play”.
We are also investigating the effect of market news, both expected and unexpected, on the currency trees.
Thanks for Listening!