Copulas in Equity and Credit Risk - Default-Dependent Intensity Models and Information-Based Setup
Deuss
Patrick
Deuss, Patrick
aut
2016-04-08
2016-05-06
en
<p>Terms, deffinitions and types of risks to which financial institutions are exposed are manifold. They
are commonly differentiated by their source or their scope of application. Risk management and
controlling departments mainly<sup>1</sup> distinguish between
<ul>
<li>market risk - e.g., equity or interest rate risk,</li>
<li>credit risk - e.g., default risk, and</li>
<li>operational risk - e.g., individual mistakes of employees.</li>
</ul>
<p>Identification of risk is sophisticated on account of the great variety of possible influencing factors.
Due to the inherent uncertainty, risk is generally measured through probabilities. Thus, mathematical
tools and schemes are frequently used for estimation and evaluation. Besides the resulting
complexity, these models must be developed, calibrated to data and numerically implemented. For
this process, conflicting standards and demands concerning
<ul>
<li> internal and strategic objectives as well as</li>
<li>regulatory requirements</li>
</ul>
<p>must be considered. Risk aggregation and measuring dependencies between risk factors are additional
issues.
In practice, these challenges are generally tackled by standard or simplified approaches. They are
less complex, their handling is
exible and numerical implementation is fast. Therefore, their known
drawbacks (e.g., under- and overestimation of risk) are accepted. In academia, many advanced
models have been developed to eliminate these failures. As consequence, practical implementation
is difficult and expensive.
In this thesis, we focus on modeling dependency structures by means of copulas<sup>2</sup>. Compared to
standard frameworks, the copula approach is more elaborate but still provides a feasible implementation.
In a mathematical nutshell, the concept states that a multivariate distribution can be split into its
one-dimensional marginal distributions and a coupling function denoted as copula. Transferred to
an economic point of view, a multidimensional problem of risk aggregation can be separated into
<ul>
<li>its single risk factors and</li>
<li>its dependency structure - i.e., its copula.</li>
</ul>
The main advantage of this idea is that single risk factors are often easily measurable. Though,
identification of dependencies is challenging. Copulas offer a large variety of dependency structures
and hence a higher degree of freedom compared to standard approaches (multivariate normal
distributions as a rule). However, the selection of the "right" copula is of central significance. In
practice, copulas already cover various scopes of applications.
The first part of this thesis introduces to the mathematical background of copulas. As application,
the value at risk of a stock portfolio is measured by the copula approach. Outcomes are compared
to a standard multivariate normal benchmark.
The second part provides an introduction to credit risk and a detailed description of so-called
intensity-based models. In this framework, we develop a new specification for modeling a copula and
default-dependent intensity. As conclusion, model construction and implementation are critically
assessed.
<br><br>
<p>----------------------------------------------------------------------------
<br><sup>1</sup>Further kinds (systemic, liquidity or model risk, for instance) exist and have ambiguous assignments to different
areas.
<br><sup>2</sup>In literature, we casually find the plural form copulae.
urn:nbn:de:hbz:468-20160506-115019-2
2016-05-06T09:45:17.158Z
2016-05-06T10:02:16.297Z
published
Diss
fbc/mathematik/diss2015/deuss