Currently, quantitative asset pricing models are often not equipped to deal with merger and acquisition events. In such cases, portfolio managers make the assumption that the model is not working and they override its decisions for an entire year. This thesis studies the performance of quantitative models after these events and provides research based guidelines for future decisions on model overrides.A selection of investment factors representing the model will be used to explain the post-event abnormal returns. In general, the data consists of monthly observations on one cross-section of firms over a time period of several years. Consequently, it may contain unobserved firm or time effects. Ignoring such effects leads to inefficient estimates and biased results. Hence, robust inference is conducted by adjusting the standard errors of a pooled regression, and through modelling the effects in a panel regression.Multiple approaches show that the separate factors are not sufficiently able to explain the abnormal returns after an event, if compared to the model's performance in regular market circumstances. Consistent results for the post-event performance are particularly hard to find. Equally weighting all factors in a single regressor, leads to model performance being equivalent to that in non-event times after 9 months, which indicates that a override period of equal length is sufficient. Therefore, the current assumption that the model is not working properly after a merger or acquisition, is correct. The robust pooled model is favoured over the panel model in this research, due to its low complexity and its straightforward results. 

Efficiently managing hedging portfolios on behalf of pension funds is key in achieving the target hedging strategy, which can significantly impact coverage ratios. A new optimization approach to fixed income portfolio management for pension funds is proposed that finds interest rate risk hedging strategies while incorporating additional requirements. These are relevant requirements for pension funds such as country allocations, low transaction costs and reasonable investment costs. In doing so, pension fund regulations and common practices are investigated in a rigorous mathematical framework. The hedging strategies are shown to perform well when back-testing. In addition, simulation of the interest rate and cash flows in a Defined Benefits pension scheme displays the good performance of the strategies. These strategies are further tailored to specific pension funds by considering the trade-off between yield and risk, which could contribute to increasing a pension fund’s coverage ratio. Alternatively, a procedure is also proposed to generate more diversified albeit less optimal hedging portfolios using the optimization approach.

Demand deposits modeling is of top importance for banking institutions and usually represents a large part of a bank portfolio. Even though these products seem rather simple at first glance, demand deposits are without a fixed maturity, generating uncertainties in the model. A significant amount of academic literature on this subject is available. However, we are experiencing negative interest rates for a few years now, that may have affected customer behavior and have led to an excess in deposits-taking for a large majority of bank. In addition to the low-rate environment, this small European bank has been growing rapidly in recent years and new customers have different characteristics from the old ones. Demand deposits modeling is therefore a major challenge for the bank. It can be divided in three steps, respectively the market rates, the deposit volumes and the deposit rates, however, only the market rates and the deposit volumes will be considered in this thesis. The dynamics of market rate follow a single factor Hull-White model. The mean-reverting parameter and the volatility are calibrated on historical data of the one-month Euribor rates, and then simulated using an exact Monte-Carlo approach. The deposit volume model is based on an Ornstein-Uhlenbeck process, where the constant drift term μ is replaced by a trend that depends on the rates' level. The trend has a different slope whether we are in a normal-rate environment or in a low-rate environment, and the probability of being in either state depends on the market rates. We create age and wealth categories for customer segmentation purpose. We then perform a cluster analysis, either using a k-means method or a hierarchical clustering algorithm, that will be included in the deposit volume model. The clustering forms similar groups of customers, reflecting better customers' diversity. Lastly, we compare two output variables, the average life and the optionality, for different simulations, one without the clustering, and two with the clustering. The best-case scenario for any bank being a high average life associated with a low optionality with regards to demand deposits modeling, the clustering integration in the model leads to more optimal results.

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. In the Dynamic Nelson-Siegel model, a Nelson-Siegel curve is fitted against the historical yield curves. The fit gives an historical series of the parameter values of the Nelson-Siegel curve, which are modelled via a stochastic process to obtain future yield curve predictions. In historical backtesting, the classic model using AR(1) processes for the parameters performs inadequate. Analysis on the underlying assumptions of the model show that the mean-reverting behaviour that is modeled is the cause. In addition the data is likely to feature heteroskedastic behaviour, which is not incorporated by the model. An adjusted model in which one parameter is modeled with a random walk with drift performs well on longer maturity rates, however shorter maturity rates are not modeled satisfactory. The Displaced Diffusion model uses a lognormal diffusion process that is shifted to model Libor rates. As it is a Libor market model, all libor rates are modelled seperately using correlated Brownian motions. The shift parameter allows negative rates to be modeled, and is initially assumed constant. The backtesting results are mixed; some observed libor rates are modeled inadequately and some cannot be rejected to come from the Displaced Diffusion model and thus are modelled correctly. When backtesting the PFE, the results are good at the short term. At the 2-year window, PFE estimates are not always conservative but the number of excesses are of medium severity when compared to the probabilities used in the green-orange-red system dictated by the Basel committee for VaR backtesting.

This thesis is a research into the relationship between performance and sales of new financial contracts of financial products providers in the employer’s market. This thesis is written in collaboration with IG&H Consulting. Combining the performance scores given by advisors on financial providers and the production of new contracts over the past two years, a logistic regression is fitted with a selected group of performance variables. The results show a significant positive effect of the performance on the production of new financial contracts. The model predicts a potential growth in the number of contracts when there is an improvement in the performance of providers in the eyes of advisors. The performance of the model is not fully satisfying but it is a good starting point. It can be ameliorated in the future with the collection of contract specific information.

Interest rate products form a large segment of over-the-counter derivatives. When the interest rate became negative, for the first time, in July 2009, interest rate models needed to adjust. Where first a log-normal model, as the Brace Gatarek Musiela (BGM) model, might have seemed logical for interest-rate products, as they were bounded by zero, now a normally distributed model, as the Hull-White model, could be considered more practical. To our knowledge, no comparison of the Hull-White model and the Brace Gatarek Musiela model has been made on the Expected Positive Exposure (EPE) (and thus Credit Valuation Adjustment (CVA)) of a swap portfolio. Therefore, this thesis compares the Hull-White model with the BGM model on the EPE of a swap portfolio. First, we show how both models can be simulated with Monte Carlo simulation and calibrated to caplets, after which we validate the used simulation. Finally, both models are compared on the convergence, computation time and EPE. It was found that the Hull-White model had a faster convergence and computation time than the BGM model for our implementation. Moreover, it was shown that the Hull-White model and BGM model have significantly different swap EPEs, except for far in-the-money (ITM) swaps and single payment swaps. Therefore, the models used for the EPE of a swap portfolio have a model risk.

This thesis showcases a rather contemporary method of solving a generalized system of stochastic differential equations (SDE's) comparable to the SABR model. The solution is derived from a stochastic-local volatility (SLV) model in which the local volatility (LV) component is kept general. This generality is maintained throughout all derivations, eventually yielding a model containing an undefined LV function. This function can then be specified however the user of the model deems suitable, as long as minor constraints are satisfied. Obviously, this is a very valuable quality of the model as it is highly customizable. The solution consists of a set of pricing functions that seemingly possess all the aforementioned desirable properties, i.e. fast in evaluation, computational tractability, flexibility etc., with little disadvantages. The generalized SLV model that is used is typically denoted in the form of two SDE's, though in the majority of this thesis an atypical three SDE form is used. This extended system is used to isolate the LV component, in turn enabling for appropriate application of an SDE transformation called the Lamperti transform, which will provide the key to solving the entire system. The Lamperti transform is a highly versatile method for transforming SDE's into new equations typically more suitable for simulation and parameter estimation procedures, and its inner-workings and various applications will be the main focus of this thesis.

In the fight against money laundering, demand for data-driven Anti-Money Laundering (AML) solutions is growing. Particularly anomaly detection algorithms have proven effective in the detection of suspicious customer behaviour, as well as observing patterns otherwise hidden in customer transaction data. In this thesis, the Isolation Forest anomaly detection algorithm is studied in combination with the model-specific local explanation method, Multiple Indicator Local Depth-based Isolation Forest Feature Importance (MI-Local-DIFFI). To expand Isolation Forest to mixed-attribute data sets, the incorporation of nominal features is explored in more detail. This analysis resulted in the introduction of Isolation Forest with Categorical Sampling (iForestCS ), a methodology that directly incorporates nominal attributes into an isolation tree without the need of encoding it onto a numerical scale. This method is tested against different encoding strategies and Isolation Forest Conditional Anomaly Detection (iForestCAD) using different synthetic data sets. The method shows improved performance to the utilization of encoding strategies for different parameters of the underlying synthetic data. Furthermore, this thesis explores the potential of ternary Isolation Forest, in which the branching strategy of an isolation tree is expanded to produce three child nodes. It is demonstrated using synthetic data, that particularly the performance of MI-Local-DIFFI reduces when applied to a ternary Isolation Forest. Finally, the research considers a practical use-case. Using customer transaction data from Triodos Bank, the locally explainable Isolation Forest is applied to mixed-attribute customer transaction data. This has provided useful insight and resulted in the detection of suspicious customer behaviour and the introduction of new rules into business practices. Although the most interesting customer behaviour did not directly emanate from the nominal attributes, the method of incorporating nominal features resulted in differences when considering the anomalies with the highest anomaly scores.

In this thesis we model extreme log-returns on economic variables and apply this to Ortec Finance's model. These extreme log-returns are relevant for risk management applications such as Value-at-Risk and other measures of tail risk. We use extreme value theory to simulate economic variables with the desired tail behaviour. We pay special attention to correlations between economic variables, since these tend to increase during financial crises. This suggest the possibility of tail dependence and we use copula theory to model behaviour similarly to what we observed historically. We find that a single parameter, the tail index, can be used to model the tail behaviour of an economic variable. To model the tail dependence between economic variables we can also use a single parameter namely the tail dependence coefficient. We model the complete dependence structure with a semiparametric copula, such that the copula has the desired tail dependence coefficient, but also approximates the dependence outside the tails. These techniques are applied in the context of vector autoregressive models, since these models are used to describe the statistical factors in Ortec Finance's Dynamic Scenario Generator, which generates future economic scenarios. We provide a first stylized indication on how these techniques could be applied in the context of Ortec Finance's model.

Machine learning methods like outlier detection are becoming increasingly more popular as tools in the fight against money laundering. In this thesis, we analyse the Isolation Forest outlier detection algorithm in detail and introduce a new local explanation method for Isolation Forest, the MI-Local-DIFFI (Multiple Indicator Local-DIFFI) method. The method uses the structure of the isolation trees and the traversal of individual outliers down the trees to determine an importance weight for each of the features. These weights are then combined into feature importance scores that are used to explain why a specific outlier is identified as such. In anti-money laundering (AML), such explanations are very valuable when determining whether an outlying customer is suspicious or not. MI-Local-DIFFI is based on a global explanation method called DIFFI and while we were conducting our research, another local version, Local-DIFFI, was also introduced. In the thesis, we use a synthetic data set to compare the performance of four different explanation methods including our MI-Local-DIFFI, Local-DIFFI and the state-of-the-art TreeSHAP method. Our MI-Local-DIFFI shows excellent results in terms of performance and runtime. Furthermore, we use a data set from Triodos bank to apply the explainable outlier detection methodology consisting of the combination of Isolation Forest and MI-Local-DIFFI. This resulted in interesting findings like the revealing of data quality issues in the current system and references to EDRs and SARs. However, after further inspection, no SARs were filed but some customers were put to higher risk classes. This procedure will be performed on a monthly basis with the goal of continuing to improve the AML processes of the bank.

In this thesis, several compound options and a real option application will be valued. First, an introduction to real options and our application will be given and bridges between financial and real options will be established. Then, an asset price model will be introduced which will be used throughout the whole thesis to value options, and several financial options will be introduced: European options, American options and compound options. If there exists a closed-form solution of the option value of these options, it will be provided and derived. When there is no closed-form solution available, numerical valuation methods should be used. The binomial method, trinomial method and Monte Carlo simulation are methods which will be explained and used in this thesis. After the introduction of these valuation methods, the results will be compared to the results obtained from the closed-form solution. When the correctness of the valuation methods methods has been confirmed, they will be used for the compound options and real option application.

In this thesis we introduce valuation techniques to price electricity storage contracts, where the electricity prices follow a structural model based on polynomial processes. In particular we focus on a Fourier-based pricing method known as the COS method, which performs impressively to price the contracts accurately. We provide details on how to formalize an electricity storage contract, taking into account the physical limitations of an electricity storage and the operational constraints of the electricity grid. In addition to the electricity storage contract, other well-known options are being considered, such as the European option, Bermudan option and Bermudan option with multiple early-exercise rights, where the same asset price model is used based on polynomial processes. We propose an approximation of the characteristic function, so that the Fast Fourier Transform (FFT) can be applied to significantly reduce the computational complexity of the COS method, which is especially suitable for pricing Bermudan options and Bermudan options with multiple early-exercise rights. With the FFT-based algorithm, the computation time of the valuation of the discussed Bermudan-type options with the COS method is reduced from seconds to milliseconds. Furthermore, the Least Squares Monte Carlo (LSMC) method is presented to value the discussed financial derivatives and used to validate the results obtained with the COS method.

This work is on the extension of the SWIFT method to option pricing problems where the sum of lognormals occurs. The SWIFT method (ShannonWavelet Inverse Fourier Technique) is extended to the valuation of geometric Asian options and arithmetic Asian options with a Lévy process as underlying price process and the valuation of European options under SABR dynamics. In both applications a sum of lognormals (or sum of increments) occurs. The main result in this thesis is the SWIFT-SIA method (SWIFT sinc integral approximation), which is applied to the valuation of arithmetic Asian options as well as to the valuation of European options under the SABRmodel. Within the SWIFT-SIA method the recovery of the probability density function is obtained by an approximation, instead of a numerical integration method, which results in a very fast method compared to an alternative method based on cosine expansions as well as high accuracy in the option values.

The Competitive Investor Game from Bell & Cover (1980) and the 푘-Player Ranking Game from Alpern & Howard (2017) are analysed in thesis. Optimal strategies have been derived and the related proofs have been given a new look. The Symmetric Multiplayer Ranking Game is considered as the general interpretation of financial competition among hedge funds. This study focused on the hedge funds that manage a Long/Short U.S. Equity strategy. Some minor evidence has been found to support the hypothesis that the studied hedge funds manage a strategy that has the objective to beat the competition in terms of annual performance in order to achieve the highest ranking.