Application Of Random Matrix Theory To The Analysis Of Financial Markets

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.

• 10,000 words – 71 pages in length
• Excellent use of literature
• Well written throughout
• Excellent use of economic models
• Ideal for economics students

1 – Introduction
Financial Markets
Currency
Markowitz Portfolio
Correlation Matrix
Hermitian Matrices
Wishart Distribution And Wishart Matrix
Random Matrices And Its Application
Density Of States
Level Density

2 – Background Reading And Motivation
Definition: Gaussian Orthogonal Ensemble
Sample Simulation On Random Matrices
Procedure
Observation
Conclusion

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

4 – Correlation Matrix After Deleting Currencies
Calculating The Revised Correlation Matrix
Investigating Eigenvalues
Investigating Eigenvectors
Analysing The Eigenvectors
Conclusion

Conclusion

References