Course description

Fundamentals of Quantitative Finance

Introduction

This course covers the fundamental econometric and numerical tools used by quantitative analysts with a focus on programming and implementation. It starts with discussing fundamental concepts and econometric analysis of financial time series and model estimation. It then moves to review calculus and linear algebra to then cover a number of methods in numerical analysis; solution of linear and nonlinear systems of equations, least squares, interpolation and approximation of functions as well as numerical differentiation and integration.

Course content

  • Introduction: The toolbox of a quantitative analyst
  • Statistics and Econometrics
    • Least squares estimation and method of moments
    • Maximum likelihood estimation (MLE)
    • Instrumental variables estimation
    • Generalized method of moments (GMM)
  • Numerical analysis
    • Numerical analysis in a nutshell
    • Linear equations and least square problems
    • Basic methods of optimization
    • Heuristic methods of optimization in a nutshell
    • Solving linear and non-linear systems
    • Interpolation and approximation of functions
    • Numerical differentiation and integration

Learning outcome knowledge

By the end of the course, the students are expected to know:

  • Linear and non-linear regressions with least squares
  • The method of moments
  • The basic idea behind maximum likelihood estimation
  • Instrumental variables estimation
  • The Generalized method of moments (GMM)
  • How to interpolate and approximate functions
  • Basic and more advanced methods optimization (constrained vs. unconstrained, one-dimensional vs. multi-dimensional, …)
  • Numerical differentiation and numerical integration

Exam organisation

  • Written assignment: 50%
  • Written exam: 50%