Value-At-Risk, Guassian distribution, Extremal distribution, Credit default swaps
This paper is motivated by empirical evidence illustrating the non-Gaussian nature of
financial returns, (Jondeau et al 2007) and analyses extreme value theory, (EVT) as a
proposed improvement (Embrechts et al., 2005) for risk estimation techniques.
Credit default swaps, (CDSís) are analysed due to their increasing important to financial
stability (European Union, 2009) and due to the lack of quantitative univariate risk
analysis of this market. EVT is generally applied to currency, equity and bond markets,
(Assaf, 2009). Whereas the majority of quantitative analysis of the CDS market has
focused on multivariate functions, analysing the dependency of CDS market returns and
other asset returns, (Chen et al., 2008). Equity and bond samples are used here as a
comparison to the CDS market returns.
The findings are divided into three parts. The first part focuses on the general
characteristics of the three asset classes, CDSís, equities and bonds, noting the nonnormality
of the distributions. As GARCH is widely used in industry to remove
dependency in the second and higher moments, the second part of the findings assesses
the efficacy of this methodology. Evidence that GARCH removes dependency in the
second moment is found but the distribution of the residuals continues to appear non-
Gaussian for all three asset classes and non-iid for the CDS sample. In light of these
findings, the third section uses a semi parametric approach to estimate the tail parameter
of the distribution of the three CDS samples. The result of the investigation suggests that
the parametric GARCH-EVT approach may be suitable for equity and bond market
univariate risk estimation but that this approach and the semi-parametric EVT approach
may both have limitations in assessing risk in CDS market returns.