Bergische Universität Wuppertal Fachbereich Mathematik und Naturwissenschaften Angewandte Mathematik - Numerische Analysis (AMNA)

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The lecture is suitable for students of mathematics as well as for economics.
The students of economathematics can use it as component AKap.NAaA-a "Selected Topics in Numerical Analysis and Algorithms" in the module of the same name.

Topics of the Lecture:

The goal of this lecture is to provide a detailed overview of Statistical/Machine Learning techniques applied to Quantitative Finance. We offer insights into the latest techniques of using such methods. Tackling topics that arise in derivatives pricing, calibration and hedging but also from time series management. This includes sophisticated modeling approaches for the Q-quant setting and nowcasting, imputation or anomaly detection for the P-quant. We give a thorough theoretical introduction but illustrate the concepts with concrete examples. Live demonstrations of the computational methods round up this course. We cover Artificial Neural Networks, Gaussian Process Regression, Gaussian Mixtures and kernel methods and their applications.

We also explain how to set up the methods in Python using various libraries such as Numpy, SciKit Learn, Keras, Tensorflow, or PyTorch. Our chosen examples are directly linked to relevant practical applications from Quantitative Finance and can be explored further after the course since all the material is available either as Python code or Jupyter notebooks.

This lecture covers the fundamentals and it illustrates the application of state-of-the-art machine learning applications for Mathematical and Quantitative Finance. We wish to bring you to the next level with our presented material.

This workshop covers the latest techniques for mastering Statistical Learning and Machine Learning methods including Neural Networks or Gaussian Process Regression and apply those to Quantitative Finance and Time Series analysis. Theoretical underpinnings are giving and explained. The material is illustrated with many relevant examples from Quantitative Finance.

• Overview of some Statistical Learning / Machine Learning techniques
• Implementation and examples from Quantitative Finance using Python/Jupyter
• Neural Networks - Architectures, Mechanics and Applications
• Generative Methods applied to Quantitative Finance
• Gaussian Process Regression in the context of pricing and time series analysis
• Gaussian Mixtures for Local Stochastic Volatility or Bermudans in multiple dimensions
• Pricing and calibration for (rough) Stochastic Volatility models such as SABR or Heston
or rough models like the rough Bergomi model
• Term structure models and Bermudan/American options
• Time Series forecasting/nowcasting and imputation using Gaussian Process Regression

Literature:

• Kienitz, Mathematics of Machine Learning, Lecture Notes, Wuppertal, SoSe 2020
• Dixon, Halperin, Bilokon, Machine Learning in Finance, Springer 2020

Previous knowledge: Analysis I - III, basic knowledge of ordinary differential equations, stochastics.

Exercises:
For the exercises we recommend to install the Python distribution from Anaconda and install the packages tensorflow, keras, pytorch, matplotlib. If other packages are necessary these can easily installed on demand.
Sheets.

Criteria: To earn credits for this course attending the lecture and successfully working on a project is obligatory. The project can either be on a theoretical aspect, i.e. assessment of a topic and working out the mathematical details, or on a practical one, i.e. by implementing a topic/algorithm/method in Python. The project should be finished by end of August 2022.