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Please use this identifier to cite or link to this item: http://hdl.handle.net/10210/125879

- roleTerm (text)
- advisor
- namePart
- Prof. F. Lombard
- roleTerm (text)
- author
- namePart
- Stander, Yolanda Sophia
- dateAccessioned
- 2012-08-15T12:45:54Z
- dateAvailable
- 2012-08-15T12:45:54Z
- dateIssued
- 2012-08-15
- dateSubmitted
- 2006
- identifier (uri)
- http://hdl.handle.net/10210/5852
- note
- M.Sc.
- abstract
- In this dissertation we take a closer look at how copulas can be used to improve the risk measurement at a financial institution. The focus is on market risk in a trading environment. In practice risk numbers are calculated with very basic measures that are easy to explain to senior management and to traders. It is important that traders understand the risk measure as that helps them to understand the risk inherent in any deal and may assist them in deciding on the optimal hedge. The purpose of a hedge is to reduce the risk in a portfolio. As senior management is responsible for deciding on the optimal risk limits and risk appetite of the financial institution, it is important for them to understand what the risks are and how to measure these. The simplicity of the risk measures leads to certain inadequacies that can have very negative consequences for a financial institution. If the risk measure does not adequately capture the risk of a deal, the financial institution may suffer big losses when there are stress events in the market. Alternatively, when the risk measure overestimates the risk of a deal, too much economic capital is tied up in the deal. This inhibits the trader from adding more deals to a portfolio that may potentially lead to big profits. Economic capital is the capital that has to be held against positions to protect the financial institution if and when extreme market moves occur. In this dissertation the focus is on how copulas can be used to improve current risk measures. We focus on bivariate copulas. Bivariate copulas are easier to depict graphically than multivariate copulas with more than two dimensions. It is also easier to prove that the fitted bivariate copulae do adequately describe the underlying dependence structure between risk factors. Even though the focus is on the bivariate case, all methodologies can easily be extended to higher dimensions. In Chapter 1 copulas are defined and some basic copula properties are shown. We consider the definition of elliptical copulas and discuss some drawbacks to using them in a financial application. Some useful Archimedean copula properties are discussed and it is shown how to generate the copula function for n 2 dimensions. The various ways in which to estimate the parameters of a copula are also discussed as well as goodness-of-fit tests that are used to test whether the copula fits the underlying data adequately. Finally the chapter ends with an example that illustrates the theory. A back-test is done to establish whether the copula adequately describes the dependence structure over time. It is also shown how the fitted copula can be used to generate stress scenarios that are used as an alternative to historical scenarios when calculating a value-at-risk (VaR) number. In chapter 2 the properties of a dependence measure are discussed and it is argued that linear correlation does not conform to these desired properties. Rank correlation measures have some additional properties that make them more efficient than linear correlation measures in certain instances. We also consider their relationship to copulas. Finally it is shown how copulas can be used in practice to get another view on the dependence structure between risk factors. In risk measurement we are mainly concerned with extreme moves that market variables may show. In chapter 3 some of the techniques used in risk management are discussed as well as some of their shortcomings. The shortcomings are addressed by applying extreme value theory to calculate stress factors and using copulas to model the dependence structure between risk factors. The theory underlying bivariate extreme copulas is discussed and illustrated with a practical example.
- languageTerm (rfc3066)
- en
- topic
- Copulas (Mathematical statistics)
- topic
- Dependence (Statistics)
- topic
- Risk management
- title
- The use of copulas in risk management.
- genre
- Mini-Dissertation

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