Exotic Derivatives and Deep Learning
This Master thesis investigates the use of Artificial Neural Networks (ANNs)for calculating present values, Value-at-Risk and Expected Shortfall of options, both European call options and more complex rainbow options. The performance of the ANN is evaluated by comparing it to a second-order Taylor polynomial using pre-calculated sensitivities to certain risk-factors. A multilayer perceptron approach is chosen based on previous literature and applied to both types of options. The data is generated from a financial risk-management software for both call options and rainbow options along with the related Taylor approximations. The study shows that while the ANN outperforms the Taylor approximation in calculating present values and risk measures for certain movements in the underlying risk-factors, the general conclusion is that an ANN trained and evaluated in accordance with the method in this study does not outperform a Taylor approximation even if it is theoretically possible for the ANN to do so. The important conclusion of the study is that the ANN seems to be able to learn to calculate present values that otherwise require Monte Carlo simulation. Thus, the study is a proof of concept that requires further development for implementation.