Introductory description

Python is a widely used programming language that is increasingly essential knowledge in the financial sector. Python dominates many modern applications, particularly in Data Science and Machine Learning. The module will use Python and Jupyter notebooks to investigate a variety of computational algorithms with the goal of solving particular problems and understanding the underlying theory.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

• Introduction to Python.

• Basic concepts in numerical computation. Computational complexity of algorithms. Order of accuracy. Numerical stability. Sources of error. Finite-differences and Taylor's Theorem. Floating point arithmetic. Algorithm design. Testing, debugging and validation.

• Introduction to Monte-Carlo methods. Central limit theorem. Monte-Carlo methods for European call and put options.

• Variance reduction techniques. Antithetic, Control variates, Importance sampling, Stratified sampling. Variance reduction for Greeks.

• Numerical methods for ordinary and stochastic differential equations. Euler and Milstein schemes. Strong and week convergence. Pricing Asian and Barrier Options.

• Introduction to Machine Learning. Supervised, unsupervised and semi-supervised learning. Loss, risk and generalisation error. Correct use of training, test and validation sets.

• Key machine learning methods (EN, PCA, PCR, RF, NN) and their performance on finance datasets.

• Neural networks. Neurons, layers, units, activation functions, connectivity. Training: back-propagation, SGD/Adam, initialization, learning rate, early stopping.

• Deep learning. Double descent. Modern topics in ML and SOTA.

Learning outcomes

By the end of the module, students should be able to:

• Deploy basic knowledge of key Machine Learning techniques and models for finance problems
• Explain different types of Machine Learning, and implement neural networks to machine learning problems
• Understand the Central Limit Theory's importance in Monte-Carlo Integration
• Estimate the complexity of an algorithm and compare the complexity of different algorithms
• Evaluate models and simulation results for reliability and accuracy
• Decompose complex problems and design step-by-step solutions
• Translate real-world problems into mathematical forms.

Indicative reading list

Reading lists can be found in Talis

Subject specific skills

Manipulate vectors and matrices, write loops, functions and complete programmes in Python
Price financial options using Monte-Carlo Integration including implementing variance reduction techniques, as well as computing associated Greeks.
Determine the accuracy of a finite-differenct numerical approximation, and understand the stability of numerical schemes and the sources of error in different numerical implementations.
Simulate stochastic ODEs, using Euler or Milstein methods, and to use these methods to price Asian and Barrier options
Classify a variety of data and make predictions using Support Vector Machines, including employing a variety of kernels.

Transferable skills

Tool Proficiency: NumPy / SciPy (numerical computations); Matplotlib / Seaborn: (data visualization); Pandas: (data manipulation); scikit-learn / TensorFlow / PyTorch: (machine learning).