dynamics of the fx market: a minimal spanning tree approach omer suleman occf and department of...

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!