This thesis presents a novel approach to the pricing of green bonds, a growing segment in financial markets with an emphasis on environmental sustainability. Unlike traditional financial instruments, green bonds uniquely incorporate environmental considerations, particularly carbon price (c_t), along with traditional factors like the short rate (r_t), into their valuation. This integration is increasingly relevant in today’s economy, reflecting a shift towards sustainable finance. The core of this research involves applying advanced numerical methods, including the Finite Difference Method, Crank-Nicolson discretization, GMRES and Bi-CGSTAB, in order to develop and analyze pricing models for both green and conventional bonds. The study aims to assess how environmental factors impact the efficiency of these numerical techniques and to compare the outcomes with conventional bond models. The research reveals that green bonds, compared to conventional bonds, present unique numerical challenges, notably requiring more iterations for convergence in iterative methods GMRES and Bi-CGSTAB because of the high carbon price volatility (σc) and the ’Greenium’ phenomenon. Moreover, the comparative analysis showed that while Bi-CGSTAB outperforms GMRES in the green bond model, the opposite is true for conventional bonds. This study not only contributes to the theoretical understanding of green bond pricing but also offers practical insights for financial analysts and investors navigating this evolving market.

Keywords: Green Bonds, Bond Pricing, Zero-Coupon Bond, Short Rate Modeling, Numerical Methods, Crank-Nicolson, GMRES, BiCGSTAB, Environmental Finance, Sustainable Investing, Comparative Analysis, Financial Modeling.

Although energy commodity price forecasting has been around for quite some time, up until recently, especially in Europe, it mostly concerned other energy commodities than gas. That is why in this work, a forecasting model is presented for the single day forecast of the daily VWAP price of the TTF month-ahead gas contract from 2020/01/02 until 2023/08/03. A model combining machine learning and data preprocessing is proposed. First a decomposition of the gas price is produced by a combination of Variational Mode Decomposition (VMD) and Independent Component Analysis (ICA). With these decompositions an initial volatility regime split is chosen because of the unusual characteristics of the dataset. During the forecasting period the Russo-Ukrainian war started, and the economy was recovering from the COVID-19 crisis, causing the gas price to surge to levels previously unknown. Using the decompositions as input, a final price prediction has been made using a Gated Recurrent Unit Neural Network (GRUNN) and Support Vector Regression (SVR), amongst others. The proposed model is compared to a selection of benchmarks, one of which is the naive forecast. To conclude, a selection of exogenous variables is added to the model to improve the performance. Gas storage and the UK NBP gas price are chosen for their specific characteristics. The best performance the model exhibits is between 0.38% MAPE for the low volatility regime, and 1.4% MAPE for the high volatility regime.

At crime scenes, various methods can be used to determine how much time has passed since the act happened, for example a body left at the scene, camera footage or eye witnesses. In this thesis, however, a different method shall be used to determine the time of the crime. The time will be determined using blood evidence.

To be exact, the goal of this thesis is to analyse the aging of bloodstains through colour analysis, and constructing a Bayesian network (BN) which can accurately make predictions on the time of deposition of a bloodstain.

The data used for the construction of the BNs was obtained from images provided by the Leiden Institute of Physics (LION). To obtain the data, the bloodstains in the images first need to be isolated from the background. Afterwards, the bloodstains are split into two parts: the inner part of the bloodstain and the complete bloodstain. Both the isolation and the splitting are done using a method called masking. Afterwards they can be converted to RGB (red, green, blue) values and using these RGB values, the following data can be collected for each colour channel of both the inner part of the bloodstain and the whole bloodstain: mean, min, max, variance, and the 5%, 20%, 50%, 80% and 95% quantiles.

Using various subsets of the data, BNs can be constructed. The structure of the BN is determined using a structure-learning algorithm called hill-climbing . To determine the validity of a given structure k-fold cross-validation can be performed using a given loss function. In this thesis, k=5 has been used, and the Mean Squared Error (MSE) has been taken as the loss function. Upon comparison of the MSE, it seems that the best model is given by the red values of a bloodstain. However, even the best performing model found in this thesis still has a considerably poor performance as the BN for the red variables has an MSE of 15149.81.