Clients with a mortgage loan may prepay a part of their loan before the contractual date. This is called prepayment. In the case of a prepayment, the bank who issued the loan earns less interest than ini- tially agreed. It is therefore essential to build accurate models for predicting prepayment behavior. In this thesis, machine learning models called artificial neural networks are used to predict conditional prepayment rates. In particular, the possibility to quantify the model uncertainty is studied. It is important to acknowledge that the accuracy of a model is not constant over its domain. Most ma- chine learning methods do not provide information about the uncertainty regarding a prediction and, unfortunately, methods that do so are often computationally expensive. This thesis studies uncertainty estimates generated by a neural network with dropout applied. Dropout is a method that randomly drops out neurons in each layer and has been suggested to prevent overfitting. We will see that this method can also be used to extract a measure of uncertainty regarding the prediction of a neural net- work efficiently. This method is used first to evaluate uncertainty for three simple functions under different distributions of the train data. Then the uncertainty estimates are evaluated for a neural network that predicts conditional prepayment rates. It will be illustrated that the uncertainty estimates provide an accurate indication of regions of the domain where predictions are inaccurate. Moreover, using a different model in the regions identified as uncertain can result in higher model performance.

In financial applications it is often necessary to determine conditional expectations in Monte Carlo type of simulations. The industry standard at the moment relies on linear regression, which is characterized by the inconvenient problem of having to choose the type and number of basis functions used to build the model, task which is made harder by the frequent impossibility to use an alternative numerical method to evaluate the "ground truth". In this thesis Gaussian Process Regression is investigated as potential substitute for linear regression, as it is a flexible Bayesian non-parametric regression model, which requires little tuning to be used. Its downfall is the computational complexity related to its "training" phase, namely cubic, which requires the use of algorithmic approximations. The most prominent approximations are reviewed and tested in different scenarios requiring the approximation
of conditional expectation by regression, among which the Longstaff-Schwartz algorithm for the pricing of Bermudan options. This thesis was carried out in cooperation with ABN-AMRO bank.

Since the last decade, we are assisting a widespread use of “black box” Machine Learning algorithms, these are algorithms with excellent performance but whose outcomes are hard to understand to a human agent. However, there are some situation when it is important to understand why a certain output is given,
and the field of explanability in Machine Learning has flourished in the last decade. In this work, we will go through some of these techniques. We will focus on model agnostic visualisation techniques introduced by Friedman (2001) and developed by Goldstein et al. (2015). Starting from the Partial Dependence plotting technique, we then analyse the Individual Conditional Expectation plot and its variants. Among them, we suggest the introduction of the so called “d-log-ICE” and we try identify scenarios where this techniques can bring better interpretability. We test our techniques on two models, the first one is based on the Boston Housing Dataset, and the second is an internal model at ABN Amro called “FLAG”.