advisor
Prof. D.J. Marais; Dr. I. Botha
author
Stander, Yolanda Sophia
2012-11-05T14:47:29Z
2012-11-05T14:47:29Z
2012-11-05
2011-10
http://hdl.handle.net/10210/8099
D.Comm.
Copulas provide a useful way to model different types of dependence structures explicitly.
Instead of having one correlation number that encapsulates everything known about the
dependence between two variables, copulas capture information on the level of dependence
as well as whether the two variables exhibit other types of dependence, for example
tail dependence. Tail dependence refers to the instance where the variables show higher
dependence between their extreme values.
A copula is defined as a multivariate distribution function with uniform marginals.
A useful class of copulas is known as Archimedean copulas that are constructed from
generator functions with very specific properties.
The main aim of this thesis is to construct multivariate Archimedean copulas by nesting
different bivariate Archimedean copulas using the vine construction approach. A characteristic
of the vine construction is that not all combinations of generator functions lead to
valid multivariate copulas. Established research is limited in that it presents constraints
that lead to valid multivariate copulas that can be used to model positive dependence
only. The research in this thesis extends the theory by deriving the necessary constraints
to model negative dependence as well. Specifically, it ensures that the multivariate copulas
that are constructed from bivariate copulas that capture negative dependence, will
be able to capture negative dependence as well. Constraints are successfully derived for
trivariate copulas. It is, however, shown that the constraints cannot easily be extended
to higher-order copulas. The rules on the types of dependence structures that can be
nested are also established.
A number of practical applications in the financial markets where copula theory can
be utilized to enhance the more established methodologies, are considered.
The first application considers trading strategies based on statistical arbitrage where
the information in the bivariate copula structure is utilised to identify trading opportunities
in the equity market. It is shown that trading costs adversely affect the profits
generated.
The second application considers the impact of wrong-way risk on counterparty credit
exposure. A trivariate copula is used to model the wrong-way risk. The aim of the
analysis is to show how the theory developed in this thesis should be applied where
negative correlation is present in a trivariate copula structure. Approaches are considered
where conditional and unconditional risk driver scenarios are derived by means of the
trivariate copula structure. It is argued that by not allowing for wrong-way risk, a
financial institutionâ€™s credit pricing and regulatory capital calculations may be adversely
affected.
The final application compares the philosophy behind cointegration and copula asset
allocation techniques to test which approach produces the most profitable index-tracking
portfolios over time. The copula asset allocation approach performs well over time;
however, it is very computationally intensive.
en
Copulas (Mathematical statistics)
Variables (Mathematics)
Asset allocation
Financial risk
Multivariate copulas in financial market risk with particular focus on trading strategies and asset allocation
Thesis