Deep Learning in Finance 7.5 credits

About the course

Module 1 (4.5 hp): Theory

The module starts with an introduction to feed-forward neural networks (FFN) and the backpropagation algorithm. Thereafter, the (stochastic) gradient descent algorithm (SGD) is investigated and applied to train FFN in the context of financial mathematics. In particular, this will be applied to solving the Black-Scholes PDE with an FFN and more general high-dimensional parabolic PDEs. This is followed by an investigation of the universal approximation theorem. After that, and in the context of financial mathematics, autoencoders (AE), generative adversarial networks (GAN), and binary classifiers alongside various layer types such as dropout layers and batch normalization layers are introduced.

In the next part of the course, all the concepts are extended by recurrent neural networks (RNN). In particular, Long-Short-Term-Memory (LSTM) and Gated-Recurrent-Units (GRU) are used.

At the end of the course, we further investigate advanced topics and choose among topics like delta hedging with possible transaction costs, stochastic optimal control, or non-Markovian modelling.

Module 2 (3 hp): Computer labs

This module covers the implementation of neural networks using Python with the PyTorch library. In particular, the applications that are studied are a selection of option pricing, optimal stopping, anomaly detection, data generation, and hedging.