## Copulas in Equity and Credit Risk - Default-Dependent Intensity Models and Information-Based Setup

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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^{1} distinguish between

- market risk - e.g., equity or interest rate risk,
- credit risk - e.g., default risk, and
- operational risk - e.g., individual mistakes of employees.

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

- internal and strategic objectives as well as
- regulatory requirements

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^{2}. 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

- its single risk factors and
- its dependency structure - i.e., its copula.

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^{1}Further kinds (systemic, liquidity or model risk, for instance) exist and have ambiguous assignments to different
areas.
^{2}In literature, we casually find the plural form copulae.