Machine Learning in Finance: Lesekurs

This notebook collects possible topics, ideas and links.

Estimation of risk with ML

The estimation of risk is a highly important topic in Mathematical Finance. Surprisingly, little is known about the estimation of risk. Here we will revisit some approaches and (hopefully) crack the open question how to estimate risk with deep neural networks.

This project already has quite a big code. We know how to efficiently estimate in certain circumstances (normal distribution, VaR, ES) and also managed to approximate the best estimator in some cases with NN. However, the empirical performance is not always good (this shall be analysed) and further estimation problems should be targeted.

This is a topic with possibly lots of work to do (could be done by 2 persons)

Literature

* Pitera/Schmidt (2018): Unbiased estimation of risk
* McNeil/Frey/Embrechts: Chapter on Backtesting and estimation of risk
* Grundmach: Code ERMAI
* Skawran: Bachelorarbeit

Deep hedging in affine models

The deep hedging approach from Bühler e.a. uses reinforcement learning to find hedging methodologies. We are interested in applying this approach in affine models and, say, on classical interest rate markets. A further goal would be to learn hedges in the case where jumps exists.

Code is already available in Lecture 3 of Josef Teichman and we need to adapt this to the new settings which we want to consider.

Literature

* Bühler, Gonon, Teichman, Wood (2018): Deep Hedging (on Arxiv)
* Föllmer/Schied: Stochastic Finance (as reference for hedging, efficient hedging, etc.)
* Filipovic (2015): Term Structure Models (as reference for affine models, term structures, etc.)

Deep Calibration