Application Of Random Matrix Theory To The Analysis Of Financial Markets (2006) Ref: econ0003 Outstanding undergraduate Dissertation 10,000 words – 71 pages Excellent use of literature Excellent use of economic models This dissertation shows the application of Random Matrix Theory (RMT) to the analysis of cross-correlation between price fluctuations of different financial assets e.g. the money market, stock market, etc. In mathematics, RMT is the study of the properties of random matrices. The mathematical properties of matrices with elements drawn from statistical distributions i.e. random matrices, determine the physical properties. The eigenvalues and eigenvectors of random matrices are often of particular interest. In this dissertation, the theory of random matrices was applied to the currency market. A cross-correlation matrix was constructed, and its eigenvalues and eigenvectors were investigated. It was found that due to a country locking its currency to another country’s currency, the eigenvalues and eigenvectors did not behave as intended. The currencies which were locking to other currencies were deleted from the data and a revised correlation matrix was constructed and its eigenvalues and eigenvectors investigated. There is no existing research on the application of RMT on currency market. So this paper is pioneering in the investigation on these models. Chapter One Introduction Definition: Financial Markets Definition: Currency Definition: Markowitz Portfolio Definition: Correlation Matrix Definition: Hermitian Matrices Definition: Wishart Distribution And Wishart Matrix Definition: Random Matrices And Its Application Definition: Density Of States Definition: Level Density CHAPTER 2 Background Reading And Motivation Definition: Gaussian Orthogonal Ensemble Sample Simulation On Random Matrices Procedure Observation Conclusion CHAPTER 3 Investigating The Currency Market Constructing The Correlation Matrix Definition: Log Return Statistics Of Correlation Matrix Distribution Of Eigenvalues Investigating The Density Of Eigenvalues Of "C" Properties Of Wishart Distribution Definition: Least Squares Conclusion Supplementary Test On Eigenvalues Hypothesis Introducing “Noise” To The Data Investigating The Eigenvectors Plotting The Eigenvectors Results Definition: Fixed Currency And Fixed Exchange Rate CHAPTER 4 Correlation Matrix After Deleting Currencies Calculating The Revised Correlation Matrix Investigating Eigenvalues Investigating Eigenvectors Analysing The Eigenvectors Conclusion CONCLUSION REFERENCES 
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