This report focus upon implied volatility for American styled Asian options, and a least squares approximation method as a way of estimating its magnitude. Asian option prices are calculated/approximated based on Quasi-Monte Carlo simulations and least squares regression, where a known volatility is being used as input. A regression tree then empirically builds a database of regression vectors for the implied volatility based on the simulated output of option prices. The mean squared errors between imputed and estimated volatilities are then compared using a five-folded cross-validation test as well as the non-parametric Kruskal-Wallis hypothesis test of equal distributions. The study results in a proposed semi-parametric model for estimating implied volatilities from options. The user must however be aware of that this model may suffer from bias in estimation, and should thereby be used with caution.

This study aims to assess which supervised statistical learning method; random forest, logistic regression or K-nearest neighbor, that is the best at predicting banks customer churn. Additionally, the study evaluates which cross-validation set approach; k-Fold cross-validation or leave-one-out cross-validation that yields the most reliable results. Predicting customer churn has increased in popularity since new technology, regulation and changed demand has led to an increase in competition for banks. Thus, with greater reason, banks acknowledge the importance of maintaining their customer base.   The findings of this study are that unrestricted random forest model estimated using k-Fold is to prefer out of performance measurements, computational efficiency and a theoretical point of view. Albeit, k-Fold cross-validation and leave-one-out cross-validation yield similar results, k-Fold cross-validation is to prefer due to computational advantages.   For future research, methods that generate models with both good interpretability and high predictability would be beneficial. In order to combine the knowledge of which customers end their engagement as well as understanding why. Moreover, interesting future research would be to analyze at which dataset size leave-one-out cross-validation and k-Fold cross-validation yield the same results.

This thesis proposes a general approach to solve the offline flight-maneuver identification problem using machine learning methods. The purpose of the study was to provide means for the aircraft professionals at the flight test and verification department of Saab Aeronautics to automate the procedure of analyzing flight test data. The suggested approach succeeded in generating binary classifiers and multiclass classifiers that identified six flight maneuvers of different complexity from real flight test data. The binary classifiers solved the problem of identifying one maneuver from flight test data at a time, while the multiclass classifiers solved the problem of identifying several maneuvers from flight test data simultaneously. To achieve these results, the difficulties that this time series classification problem entailed were simplified by using different strategies. One strategy was to develop a maneuver extraction algorithm that used handcrafted rules. Another strategy was to represent the time series data by statistical measures. There was also an issue of an imbalanced dataset, where one class far outweighed others in number of samples. This was solved by using a modified oversampling method on the dataset that was used for training. Logistic Regression, Support Vector Machines with both linear and nonlinear kernels, and Artifical Neural Networks were explored, where the hyperparameters for each machine learning algorithm were chosen during model estimation by 4-fold cross-validation and solving an optimization problem based on important performance metrics. A feature selection algorithm was also used during model estimation to evaluate how the performance changes depending on how many features were used. The machine learning models were then evaluated on test data consisting of 24 flight tests. The results given by the test data set showed that the simplifications done were reasonable, but the maneuver extraction algorithm could sometimes fail. Some maneuvers were easier to identify than others and the linear machine learning models resulted in a poor fit to the more complex classes. In conclusion, both binary classifiers and multiclass classifiers could be used to solve the flight maneuver identification problem, and solving a hyperparameter optimization problem boosted the performance of the finalized models. Nonlinear classifiers performed the best on average across all explored maneuvers.