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 Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson, M McDonald, S Williams, S Howison

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Page 1: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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

Page 2: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

NetworksWorld Wide Web Yeast Proteins

High School Dating Stock Market

Page 3: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Networks

Fully Connected Network

Cyclic Network Tree: Acyclic Network

Page 4: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 5: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 6: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 7: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 8: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 9: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

MST in Finance – Equity Market

Mantegna, J-P Onnela et. al.

Page 10: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

MST in Finance – Hedge Funds

Miceli and Susinno

Page 11: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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?

Page 12: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 13: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Trees of Hourly Data

Page 14: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Gold Cluster

Page 15: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

AUD Cluster

Page 16: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Spurious Correlations? Triangle Effect

Correlation of returns:

Page 17: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Comparison of Real and Random Trees

Currency MST for 1993-94 Intersection of real and random MST for 1993-94

Page 18: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Degree Distributions

Page 19: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Dynamic MSTs

Page 20: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Stability of MST

0 500400300200100

1.00

0.82

0.90

dt

Single step survival ratio

Page 21: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Multi-step Survival of Links

1.0

0

5000 1000 1500 2000 2500 3000 4000 4500

Page 22: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Dynamics of JPY Cluster

Page 23: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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

Page 24: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

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.

Page 25: Dynamics of the FX Market: A Minimal Spanning Tree Approach Omer Suleman OCCF and Department of Physics University of Oxford Collaborators: N F Johnson,

Thanks for Listening!