Dependence Modeling for Operational Risks

Master Thesis in "Risk Management and Regulation", Frankfurt (2016)


Modelling of Credit Spread Risk - in consideration of Migration Risk

Master Thesis in "Mathematical Finance", Oxford (2015)

With the publication of the final version of the Basel Committee's Fundamental review of the trading book (FRTB) in 2015/2016 banks will have to reorganise their measurement of credit risk and implement an integrated migration and spread risk model to calculate the Integrated Credit Spread Risk Capital Charge (CSR). In the course of this work we will present and develop a consistent athematical framework to calculate the CSR by transforming and extending current common market practice models for the measurement of migration risk to additionally account for credit spread risk. Making use of the same input data as current credit portfolio models the presented approach could prove to be an attractive opportunity for banks to implement latest regulatory requirements based on input data already processed and available. In the course of this work we will review the relevant regulatory requirements. We will present a standard credit portfolio model considering migration and default risk which will serve as the basic model throughout this work and will be transformed to additionally account for credit spread risk thereafter. Here, we make use of the pearson distribution family - a distribution family which is able to capture the highly skewed and fat-tailed shapes of credit risk distributions. Furthermore, validation methods - and for the case of unsatisfactory validation results - further model extensions are introduced. We perform several simulation studies to show that the specied approach works as designed and is suitable to model credit spread and migration risk in an integrated way.


Modelling behavioural effects in stock markets

Master Thesis in "Mathematical Finance", Oxford (2014)

In this work behavioural effects on stock market prices are investigated. Starting from fundamental considerations on behavioural effects, the starting point to model these effects is the model developed by Caginalp and Balenovich. It is investigated in which ways the model should be extended to capture important points which are not modelled yet. In stock markets stylized facts, especially scaling laws, are important. Thus it is also investigated, whether and in which ways the model predicts these, and in which way they are modelled.

Liquidity-at-Risk using Extreme Value Theory - a critical assessment

Master Thesis in "Mathematical Finance", Oxford (2012)

The presented thesis focuses on Liquidity-at-Risk (LaR) based on the peak-over-threshold (POT) method. This stress figure is motivated by the fact, that liquidity risk is located in the extreme tails of the distribution of the autonomous account movements. Therefore standard methods for risk assessment fail to capture all aspects of the inherited risk correctly. As the POT-method explicitly focuses on the tail-behavior of a distribution it is better suited to estimate liquidity risk than other approaches, e.g. standard quantile estimator based on a normal distribution. Nevertheless the POT-method has still some major drawbacks, e.g. its limited usability as a control instrument for liquidity risk, which are examined next. It is then concluded that the strength of the LaR using POT is the possibility to calculate the amount of liquid assets, that must be available to prevent insolvency with some confidence level. Thus it helps to fulfill one fundamental requirement of all legal texts. But as soon as more information, e.g. for management decisions, are to be extracted from LaR it becomes awkward.

An Integrated View on Market and Credit Risk

Master Thesis in "Mathematical Finance", Oxford (2012)

In this thesis we present an integrated approach to market and credit risk modeling that offers the possibility to consider interest rate risk, credit spread risk, migration and default risk within a consistent theoretical framework. The contribution of this work is to link the interest rate and credit spread evolution to the migration and default risk by a structural credit portfolio model. In the standard approach to credit risk modeling, the dynamic of rating transitions is not intrinsically linked to the stochastic evolution of credit spreads. Furthermore, conventional migration-mode models have only limited potentialto produce reasonable spread distributions which motivates the need for more elaborate models. In our model, credit state and credit spread evolution are driven by the same underlying process. This incorporates the joint simulation of credit states and interest rates at the risk horizon. The issuer’s spread term structure at the risk horizon is generated by an asset value threshold model. It is derived from the first passage time density for the asset value hitting a lower stochastic barrier. Therefore, an extended structural term structure model is embedded into a multi-factor framework to simulate the joint evolution of issuer credit states. We focus our analysis on changes in market values due to changes in the credit states and the associated issuer specific credit spread curves as well as the risk-free interest rate curves. Thus, the integratedportfolio model incorporates credit risk associated with migration and defaults with stochastic recovery rates, systematic and idiosyncratic credit spread risk as well as stochastic interest rate risk. We perform a simulation study to show that the specified model reproduces the stylized facts of the credit spread term structure and can model migration and default risk properly.