Solving multivariate expectations using dimension-reduced fourier-cosine series expansion and its application in finance

The computation of multivariate expectations is a common task in various fields related to probability theory. This thesis aims to develop a generic and efficient solver for multivariate expectation problems, with a focus on its application in the field of quantitative finance, specifically for the quantification of Counterparty Credit Risk (CCR...

An integrated benchmark model for Counterparty Credit Risk

The EAD metric is widely used in the calculations for the capital requirements concerning Counterparty Credit Risk (CCR). In this thesis we compare several methods for calculating this EAD. Basel III gives us two methods, the Standardized Approach for CCR (SA-CCR) and the Internal Model Method (IMM). Furthermore, we introduce an integrated...

Replacing the Monte Carlo Simulation with the COS Method for PFE (Potential Future Exposure) Calculations

To fulfil the need in the industry for fast and accurate PFE calculations in practice, a new, semi-analytical method of calculating the PFE metric for CCR has been developed, tested and analyzed in this thesis. Herewith we focus on the calculation of PFEs for liquid IR and FX portfolios involving up to three correlated risk-factors: a domestic...

Urn models and other approaches to risk and tails, with applications in risk management and climatology

This dissertation collects three scientific contributions, already published in international peer-reviewed journals, plus some extra considerations and work-in-progress. First, we present a model based on reinforced urn processes, which conjugates to the right-censored recovery process, and empirically apply it to the time series of recovery...

Fast Calculations of Portfolio Credit Losses and Sensitivities

Computing portfolio credit losses and associated risk sensitivities is crucial for the financial industry to help guard against unexpected events. Quantitative models play an instrumental role to this end. As a direct consequence of their probabilistic nature, portfolio losses are usually simulated using Monte Carlo copula models, which in turn...

Interest rate models for estimating counterparty credit risk: Dynamic Nelson-Siegel and Displaced Diffusion

In this study, two interest rate models are analysed in context of counterparty credit risk. The goal of the study is to find a model that performs well on historical simulation for the PFE and EPE. The two models analysed are the Dynamic Nelson-Siegel model and the Displaced Diffusion model.<br/>In the Dynamic Nelson-Siegel model, a Nelson...

Assessing concentration and diversification in portfolio credit risk models

This thesis explores existing and proposes new methods for assessing concentration risk in default-only credit risk models. Within the existing methods, the analytic Granularity Adjustment is studied in the single factor Gaussian threshold and in the CreditRisk+ framework. These adjustments are tested on a sample portfolio in the presence of...

A battle of pooled and panel data in credit risk modelling

When dealing with datasets where the observations are obtained from the same cross-sectional units at multiple time points, most of the times, heterogeneity arises across he cross-sectional units. If one ignores this heterogeneity, assuming that the data are pooled, the parameters estimations run the risk of being inconsistent. This thesis...

Modelling Low Default Portfolios

This thesis is on the subject of modelling the probability of default in a low default portfolio. In these portfolios there is a high risk of underestimating the true probability of default. Two models are considered, a Gaussian one factor model and a Poisson model with Gamma mixture. Classical estimation methods as the maximum likelihood are...

Stability-Based Model Selection in Non-Stationary Environment

Model selection is associated to model assessment, which is the problem of comparing different models, or model hyperparameters, for a particular learning task. It constitutes a fundamental step in building machine learning models. The central question is: How a model will work in the future? In this thesis, a new model selection scheme for...

Optimale importance sampling in Markovketens: Efficiënte simulatie zeldzame gebeurtenissen

Toepassing importance sampling op credit risk probleem met onafhankelijke schuldenaren.

Interest Rate Modelling for Counterparty Credit Risk

In this thesis we describe a general framework to determine counterparty credit risk. Interest rates as risk factor will in this framework be generated by a Monte Carlo simulation and described by means of a stochastic model. We describe three equilibrium models that can apply the interest rate simulation. The characteristics of these models on...

Continuous Term Structures for Implied Recovery

Credit risk pricing models assume recovery to be at its \textit{historical} average (historical recovery assumption). However, the effect of this assumption is not completely understood. The heard of this thesis lies in constructing a new pricing model for Credit Default Swaps (CDS), in particularly allowing for negative correlation between...

Credit Value Adjustment for Multi-Asset Options

This thesis works on the efficient quantification of counterparty credit risk.

A Benchmark Approach of Counterparty Credit Exposure of Bermudan Option under Lévy Process: The Monte Carlo-COS Method

An advanced method, which we call Monte Carlo-COS method, is proposed for computing the counterparty credit exposure profile of Bermudan options under Lévy process. The different exposure profiles and exercise intensity under different mea- sures, P and Q, are discussed. Since the COS method [1] delivers accurate Bermudan prices, and no change...

Higher order saddlepoint approximations in the Vasicek portfolio credit loss model

This paper utilizes the saddlepoint approximation as an efficient tool to estimate the portfolio credit loss distribution in the Vasicek model. Value at Risk (VaR), the risk measure chosen in the Basel II Accord for the evaluation of capital requirement, can then be found by inverting the loss distribution. VaR Contribution (VaRC), Expected...