Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantitative Methods in Finance

Eric Vansteenberghe

TL;DR

This course material delivers a structured, code-oriented introduction to Quantitative Methods in Finance, blending probability, statistics, numerical methods, and empirical modeling with Python and R. It emphasizes reproducible computation, data handling, time-series analysis (including SARIMAX and GARCH), risk modeling, and econometric concepts like VARs and event studies, while situating econometrics within the broader ML landscape. Practical content spans Monte Carlo methods, Copulas, Cholesky-based multivariate simulations, and data-assembly pipelines from central banks and financial data sources. The notes aim to enable replication of state-of-the-art empirical work and to equip applied researchers with transparent, rigorous tools for forecasting, risk assessment, and empirical analysis in finance and macro-finance.

Abstract

These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit combining probability theory, statistics, numerical methods, and empirical modeling, with a strong emphasis on implementation in Python. Core topics include random variables and distributions, moments and dependence, simulation and Monte Carlo methods, numerical optimization, root-finding, and time-series models commonly used in finance and macro-finance. Particular attention is paid to translating theoretical concepts into reproducible code, emphasizing vectorization, numerical stability, and interpretation of outputs. The notes progressively bridge theory and practice through worked examples and exercises covering asset pricing intuition, risk measurement, forecasting, and empirical analysis. By focusing on clarity, minimal prerequisites, and hands-on computation, these lecture notes aim to serve both as a pedagogical entry point for non-programmers and as a practical reference for applied researchers seeking transparent and replicable quantitative methods in finance.

Quantitative Methods in Finance

TL;DR

This course material delivers a structured, code-oriented introduction to Quantitative Methods in Finance, blending probability, statistics, numerical methods, and empirical modeling with Python and R. It emphasizes reproducible computation, data handling, time-series analysis (including SARIMAX and GARCH), risk modeling, and econometric concepts like VARs and event studies, while situating econometrics within the broader ML landscape. Practical content spans Monte Carlo methods, Copulas, Cholesky-based multivariate simulations, and data-assembly pipelines from central banks and financial data sources. The notes aim to enable replication of state-of-the-art empirical work and to equip applied researchers with transparent, rigorous tools for forecasting, risk assessment, and empirical analysis in finance and macro-finance.

Abstract

These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit combining probability theory, statistics, numerical methods, and empirical modeling, with a strong emphasis on implementation in Python. Core topics include random variables and distributions, moments and dependence, simulation and Monte Carlo methods, numerical optimization, root-finding, and time-series models commonly used in finance and macro-finance. Particular attention is paid to translating theoretical concepts into reproducible code, emphasizing vectorization, numerical stability, and interpretation of outputs. The notes progressively bridge theory and practice through worked examples and exercises covering asset pricing intuition, risk measurement, forecasting, and empirical analysis. By focusing on clarity, minimal prerequisites, and hands-on computation, these lecture notes aim to serve both as a pedagogical entry point for non-programmers and as a practical reference for applied researchers seeking transparent and replicable quantitative methods in finance.
Paper Structure (826 sections, 5 theorems, 1027 equations, 4 figures, 12 tables)

This paper contains 826 sections, 5 theorems, 1027 equations, 4 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Which tools are allowed to be used for this lecture?
  3. What type of computer do I need for this lecture, do I need to pay for an LLM?
  4. What is expected out of these lectures?
  5. Disclaimer
  6. Projects and evaluation
  7. Some notes on ethics
  8. First semester: a first step toward a master thesis
  9. Pen an paper
  10. Coding grade
  11. Final report for (tbd) midnight
  12. Question to be addressed
  13. Some remarks about the final report and code
  14. Second semester: to be announced
  15. Quantitative methods with R or python
  16. ...and 811 more sections

Key Result

Theorem 1

For a certain class of distributionsThis class regroup all classical continuous distributions., the $GPD$ is the limit distribution for the excess distribution when the threshold tends to $x_F$. Formally, we can find a positive and measurable function $\beta(u)$ such that if and only if, $F\in MDA(H_\xi)$.

Figures (4)

  • Figure 1: Empirical cumulative distribution functions (cdfs) of realized annual earnings for veterans (red) and non-veterans (blue).
  • Figure 2: Estimated cumulative distribution functions (cdfs) of potential earnings for compliers, obtained via instrumental variable methods (using equations (5) and (6)). The horizontal axis represents annual earnings thresholds, while the vertical axis shows the cumulative probability that a complier's earnings are below a given level. The two curves correspond to the estimated distributions if all compliers were treated (veterans) versus untreated (non-veterans). The gap in the lower tail indicates that military service mainly reduces earnings among low earners, even though the average difference may be small.
  • Figure 3: Differences-in-Differences visual
  • Figure :

Theorems & Definitions (7)

  • Theorem 1
  • Definition 77.1
  • Theorem 2
  • Theorem 3
  • Corollary 3.1
  • Definition 77.2
  • Theorem 4