ComputationalFinance

Repository for the computational finance module in the Southampton Data Science Masters

Aims and Objectives

Demonstrate knowledge and understanding of:

• The concepts underlying computational finance
• The mathematical tools, and their computational implementations underlying the subject.
• Implement a simulated fund management system that uses real-life data from the stock exchange.

Syllabus:

1. Mathematical preliminaries

   • Numerical analaysis
   • Optimization
   • Stochastic differential equations
   • Monte-Carlo simulations

2. Software preliminaries

   • MATLAB
   • Finance tollbox in MATLAB
   • Other tools - overview of R and packages

3. Financial instruments and their uses

4. Portfolio opimization

   • Utility theory
   • Quantifying risk

5. Options Pricing

   • Black-Scholes model
   • Options pricing by Monte Carlo methods

CW1: Portfolio Optimisation (Specification Report Grade: 30/30)

This cousework aimed to analyse standard methods of producing efficient portfolios:

• A naive, evenly spread portfolio.
• Using the efficient frontier.
• A greedy sparse index tracking algorithm.
• A regularised sparse index tracking algorithm.

Each of these were computed on historic data and the results were compared / critically analysed, discussing where each succeeds and fails as well as how they differ in theory vs. practice.

CW2: Options pricing (Specification Report Grade: 30/30)

This coursework looks at computing options pricing using Black-Scholes and Binomial lattice methods. This is compared to real data and the limits of these methods are discussed: observing volatility smiles, comparing the differences between European and American options and methods for estimating volatility.

CW3 Non-parametric options pricing (Specification Report Grade: 15/15)

In this coursework we consider learning options pricing through a neural network approach. We train historic data using a gaussian mixture model. We discuss the effecitveness of such models and the contrast with parametric simpler models from the previous coursework.

CW4 Kalman Filtering and Lasso Regularisation (Specification Report Grade: 25/25)

In this coursework we build a Kalman filter to filter the noise from historic index prices. We investigate the residuals of this filter to link them to econometric variables such as oil price. To do this a lasso regularisation model is built.