Quantitative methods for finance

The course opens with the different types of data used in finance and their associated issues, including the standards and conventions needed to handle them correctly (e.g. ISO 8601, time zones, and date/time handling in R). After examining the cross-section and temporal aggregation properties of returns, it addresses the estimation of the variance-covariance matrix (including the single-index model) and the empirical risk-return characteristics —and volatility behavior— of the main asset classes. Decision theory is then introduced, in particular expected utility theory, followed by the mean-variance optimization model, the properties of frontier portfolios, and the CAPM. Finally, after some remarks on portfolio and investment fund management, the course presents the lognormal price model and techniques for computing Value at Risk and Conditional Value at Risk, both parametric and via historical simulation.

The course pursues three objectives:

1. Study selected financial models for asset allocation and risk measurement;
2. Understand the issues involved in identifying and using various types of financial data;
3. Illustrate, with real data, simple applications of the mathematical tools underlying these models.

In presence

Students will work through practical issues such as sourcing and processing financial data and interpreting the results —and limitations— of the mean-variance optimization model. The R statistical software is used extensively, both in examples with real data and in in-class exercises.

Depending on the number of students enrolled, the exam will be held in oral or written form.