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Clustering in Financial Markets: A Network Theory Approach
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2014 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Klusteranalys och grafpartitionering i finansiella nätverk (Swedish)
Abstract [en]

In this thesis we consider graph partition of a particular kind of complex networks referred to as power law graphs. In particular, we focus our analysis on the market graph, constructed from time series of price return on the American stock market. Two different methods originating from clustering analysis in social networks and image segmentation are applied to obtain graph partitions and the results are evaluated in terms of the structure and quality of the partition. Along with the market graph, power law graphs from three different theoretical graph models are considered. This study highlights topological features common in many power law graphs as well as their differences and limitations.

Our results show that the market graph possess a clear clustered structure only for higher correlation thresholds. By studying the internal structure of the graph clusters we found that they could serve as an alternative to traditional sector classification of the market. Finally, partitions for different time series was considered to study the dynamics and stability in the partition structure. Even though the results from this part were not conclusive we think this could be an interesting topic for future research.

Abstract [sv]

I denna uppsats studeras graf partition av en typ av komplexa nätverk som kallas power law grafer. Specifikt fokuserar vi på marknadengrafen, konstruerad av tidsserier av aktiepriser på den amerikanska aktiemarknaden. Två olika metoder, initialt utvecklade för klusteranalys i sociala nätverk samt för bildanalys appliceras för att få graf-partitioner och resultaten utvärderas utifrån strukturen och kvaliten på partitionen. Utöver marknadsgrafen studeras aven power law grafer från tre olika teoretiska grafmodeller. Denna studie belyser topologiska egenskaper vanligt förekommande i många power law grafer samt modellerns olikheter och begränsningar.

Våra resultat visar att marknadsgrafen endast uppvisar en tydlig klustrad struktur för högre korrelation-trösklar. Genom att studera den interna strukturen hos varje kluster fann vi att kluster kan vara ett alternativ till traditionell marknadsindelning med industriella sektorer. Slutligen studerades partitioner för olika tidsserier för att undersöka dynamiken och stabiliteten i partitionsstrukturen. Trots att resultaten från denna del inte var entydiga tror vi att detta kan vara ett intressant spår för framtida studier.

Place, publisher, year, edition, pages
2014.
Series
TRITA-MAT-E, 2014:54
Keyword [en]
Complex networks, cluster analysis, graph partition, market graph, power law graphs, random graphs
Keyword [sv]
Komplexa nätverk, klusteranalys, graf partition, marknadsgrafen, power law grafer, slumpmässiga grafer
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-150577OAI: oai:DiVA.org:kth-150577DiVA: diva2:754673
External cooperation
Center for Applied Optimization, University of Florida
Subject / course
Optimization and Systems Theory
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2014-10-10 Created: 2014-09-06 Last updated: 2014-10-10Bibliographically approved

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