This
dissertation shows the application of Random Matrix Theory (RMT)
to the analysis of crosscorrelation 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 crosscorrelation 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
Chapter 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
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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