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Quant finance lecture notes

97 lecture notes selected for learning quantitative finance. Highlighted picks come first.

1. A Brief Introduction to Stochastic Calculus (Columbia IEOR E4706)

   Martin Haugh

   brownian motion · calculus · stochastic calculus · stochastic processes

2. A Course in Stochastic Game Theory

   Eilon Solan · 2022

   Cambridge University Press · Game Theory · Mathematics · Stochastic Game Theory, Stochastic Games · Tel Aviv University

3. A Forward Looking View of Factor Investing

   Chuan Shi

   asset pricing · econometrics · factor investing · machine learning

4. A Succinct Summary of Reinforcement Learning

   Sanjeevan Ahilan · 2023

   Key Results · Reinforcement Learning · Review · Single-Agent RL · Summary

5. Algorithms for Artificial Intelligence

   Dorsa Sadigh, Percy Liang, Robert J. Moss

   algorithms · machine learning · neural networks · optimization · regression

6. All of Statistics

   Larry Wasserman · 2004

   CMU · Inference · Mathematical Statistics · Probability · Springer · Statistics

7. Black-Scholes and the Volatility Surface

   Martin Haugh · 2013

   black-scholes · delta hedging · implied volatility · martingale pricing · option greeks · risk-neutral pricing

8. Calculus for Mathematicians, Computer Scientists, and Physicists

   Andrew D. Hwang · 2020

   Abstract Mathematics · Calculus · Mathematics for Computer Scientists & Physicists

9. Credit Modeling and Credit Derivatives (Columbia IEOR E4706)

   Martin Haugh

   credit risk · derivatives · financial engineering · mathematical finance · option pricing

10. CS229 Machine Learning: Course Notes

    Andrew Ng, Stanford University

    algorithms · machine learning · regression · reinforcement learning

11. CS229 Machine Learning: Supervised Learning

    Andrew Ng, Stanford University

    algorithms · machine learning · optimization · regression

12. Deterministic Cash-Flows (Columbia IEOR E4706)

    Martin Haugh

    interest rates · mathematical finance

13. Factor Failure

    Chuan Shi

    asset pricing · factor investing

14. Financial Econometrics — 2023 Lecture Notes

    Rauli Susmel

15. Financial Econometrics Notes

    Kevin Sheppard, University of Oxford · 2020

    Econometrics · Finance · Financial Econometrics · Time Series · University of Oxford

16. Forwards, Swaps, Futures and Options (Columbia IEOR E4706)

    Martin Haugh

    derivatives · financial engineering · mathematical finance

17. Foundations of Financial Engineering: Assignment 1 (Columbia, 2016)

    Martin Haugh

    derivatives · financial engineering · mathematical finance · risk management

18. Foundations of Financial Engineering: Assignment 10 (Columbia, 2016)

    Martin Haugh

    financial engineering · fixed income · interest rates · mathematical finance

19. Foundations of Financial Engineering: Assignment 2 (Columbia, 2016)

    Martin Haugh

    asset pricing · derivatives · financial engineering · martingales · mathematical finance · option pricing

20. Foundations of Financial Engineering: Assignment 3 (Columbia, 2016)

    Martin Haugh

    asset pricing · derivatives · financial engineering · martingales · mathematical finance · option pricing

21. Foundations of Financial Engineering: Assignment 4 (Columbia, 2016)

    Martin Haugh

    asset pricing · derivatives · financial engineering · fixed income · interest rates · mathematical finance

22. Foundations of Financial Engineering: Assignment 5 (Columbia, 2016)

    Martin Haugh

    asset pricing · capm · financial engineering · market risk · mathematical finance · optimization

23. Foundations of Financial Engineering: Assignment 6 (Columbia, 2016)

    Martin Haugh

    brownian motion · financial engineering · martingales · mathematical finance · probability · stochastic calculus

24. Foundations of Financial Engineering: Assignment 7 (Columbia, 2016)

    Martin Haugh

    asset pricing · derivatives · financial engineering · martingales · mathematical finance · option pricing

25. Foundations of Financial Engineering: Assignment 8 (Columbia, 2016)

    Martin Haugh

    credit risk · derivatives · financial engineering · mathematical finance · probability · stochastic processes

26. Foundations of Financial Engineering: Assignment 9 (Columbia, 2016)

    Martin Haugh

    financial engineering · mathematical finance · option pricing · real options

27. High-Dimensional Statistics

    Jan-Christian Hütter, Philippe Rigollet · 2023

    concentration inequalities · high-dimensional statistics · matrix estimation · minimax estimation · nonparametric statistics · regression

28. Implied Volatility Surface

    Martin Haugh · 2013

    black-scholes · delta hedging · greeks · implied volatility · option pricing · risk-neutral pricing

29. Intro to Factor Investing

    Chuan Shi

    asset pricing · factor investing

30. Introduction to Algorithms (second edition)

    Charles E. Leiserson, Clifford Stein, Ronald L. Rivest · 2001

    algorithm analysis · algorithm design · algorithms · computational complexity · data structures · divide and conquer

31. Introduction to Real Options (Columbia IEOR E4706)

    Martin Haugh

    financial engineering · mathematical finance · real options

32. Lecture 10: Change Of Measure And The Girsanov Theorem (UChicago, 2001)

    Steven P. Lalley

    brownian motion · martingales · mathematical finance · probability · stochastic calculus · stochastic processes

33. Lecture 2: Multiperiod Models And Trees (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance

34. Lecture 5: Brownian Motion (UChicago, 2001)

    Steven P. Lalley

    brownian motion · mathematical finance · probability · stochastic processes

35. Lecture 6: The Itô Calculus (UChicago, 2001)

    Steven P. Lalley

    brownian motion · calculus · mathematical finance · probability · stochastic calculus · stochastic processes

36. Lecture 7: Black–Scholes Theory (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance · option pricing · stochastic calculus · stochastic differential equations

37. Lecture 8: The Cameron–Martin Formula and Barrier Options (UChicago, 2001)

    Steven P. Lalley

    brownian motion · derivatives · martingales · mathematical finance · option pricing · probability

38. Lecture 9: A Model For Foreign Exchange (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · foreign exchange · mathematical finance · probability · stochastic calculus

39. Lectures 3 And 4: Martingales (UChicago, 2001)

    Steven P. Lalley

    asset pricing · martingales · mathematical finance · probability · stochastic processes

40. Machine Learning: a Lecture Note

    Kyunghyun Cho · 2025

    Genentech · Lecture Notes · Machine Learning · NYU

41. Martingale Pricing Theory in Discrete-Time and Discrete-Space Models (Columbia IEOR E4706)

    Martin Haugh

    asset pricing · financial engineering · martingales · mathematical finance

42. Math 290-1: Linear Algebra & Multivariable Calculus Lecture Notes

    Santiago Cañez

    eigenvalues · gauss-jordan elimination · linear algebra · linear systems · matrices · multivariable calculus

43. Mathematical Finance 345 / Statistics 390: Homework 1 (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance · option pricing

44. Mathematical Finance 345 / Statistics 390: Homework 2 (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance · option pricing

45. Mathematical Finance 345 / Statistics 390: Homework 3 (UChicago, 2001)

    Steven P. Lalley

    martingales · mathematical finance · probability · stochastic processes

46. Mathematical Finance 345 / Statistics 390: Homework 4 (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · martingales · mathematical finance · probability · stochastic processes

47. Mathematical Finance 345 / Statistics 390: Homework 5 (UChicago, 2001)

    Steven P. Lalley

    brownian motion · probability · stochastic processes

48. Mathematical Finance 345 / Statistics 390: Homework 6 (UChicago, 2001)

    Steven P. Lalley

    brownian motion · mathematical finance · probability · stochastic calculus · stochastic differential equations · stochastic processes

49. Mathematical Finance 345 / Statistics 390: Homework 7 (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance · option pricing · stochastic calculus · stochastic processes

50. Mathematical Finance 345 / Statistics 390: Homework 8 (UChicago, 2001)

    Steven P. Lalley

    asset pricing · brownian motion · derivatives · mathematical finance · option pricing · probability

51. Mathematical Finance 345 / Statistics 390: Homework 9 (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance · option pricing · probability · stochastic calculus

52. Mathematical Foundations of Machine Learning

    Robert Nowak · 2022

    bayesian inference · kernel methods · neural networks · optimization · probability · statistical learning theory

53. Mathematics of Computational Finance

    Andrzej Palczewski, University of Warsaw · 2022

    american options · computational finance · derivative pricing · finite difference methods · finite element methods · monte carlo methods

54. Maths You Need for Graduate Studies in Quantitative Finance

    Alexandre Landi

    linear algebra

55. Matrix Calculus (for Machine Learning and Beyond)

    Alan Edelman, Paige Bright, Steven G. Johnson · 2023

    Course Notes · Linear Algebra · MIT · Machine Learning · Matrix Calculus

56. Max Dama on Automated Trading

    Max Dama · 2011

    Algorithms · Automated Trading · Quantitative Trading

57. Mean-Variance Optimization and the CAPM (Columbia IEOR E4706)

    Martin Haugh

    asset pricing · capm · mathematical finance · optimization · portfolio management · portfolio optimization

58. Multiple Hypothesis Testing

    Chuan Shi

    factor investing · hypothesis testing · probability · statistical inference · statistics

59. Notes on Quantitative Finance

    Jimmy Qin · 2019

    derivatives · forwards · futures · interest rates · no-arbitrage · options

60. Optimization Methods in Finance

    Gerard Cornuejols, Reha Tütüncü · 2006

    CMU · Carnegie Mellon · Finance · Mathematical Finance · Optimization

61. Other Topics in Quantitative Finance (Columbia IEOR E4706)

    Martin Haugh

    corporate finance · financial engineering

62. Poisson Processes (Chapter 9)

    David Pollard

    probability · statistics · stochastic processes

63. Portfolio Sort Analysis

    Chuan Shi

    asset pricing · factor investing

64. Princeton Measure Theory

    Princeton University, Shapiro · 2025

    Lecture Notes · Measure Theory · Princeton · Real Analysis

65. Probability & Markets

    Jane Street

    adverse selection · conditional probability · confidence intervals · counting · expected value · financial markets

66. Quant Trading Guide

    Callum McDougall · 2020

    algorithmic trading · financial markets · internships · market making · math interviews · probability puzzles

67. Regression-Based Test

    Chuan Shi

    asset pricing · econometrics · factor investing · hypothesis testing · regression · statistical inference

68. Statistics Cheatsheet With Python Codes and Visualization

    soorabcode · 2025

    anova · bayes theorem · binomial distribution · confidence intervals · correlation · data science

69. Stochastic Calculus - An Introduction with Applications

    Gregory F. Lawler · 2015

    Brownian motion · Itô calculus · applications in finance · continuous-time models · martingales · probability theory

70. Stochastic Calculus: Class 11 — Ito (NYU, 2019)

    Jonathan Goodman

    brownian motion · calculus · stochastic calculus · stochastic differential equations · stochastic processes

71. Stochastic Calculus: Class 12 — Ito, theory (NYU, 2019)

    Jonathan Goodman

    brownian motion · calculus · probability · stochastic calculus · stochastic processes

72. Stochastic Calculus: Class 13 — change of measure (NYU, 2019)

    Jonathan Goodman

    brownian motion · calculus · probability · stochastic calculus · stochastic processes

73. Stochastic Calculus: Class 2 — Brownian motion and diffusion equations (NYU, 2019)

    Jonathan Goodman

    brownian motion · calculus · partial differential equations · probability · stochastic calculus · stochastic processes

74. Stochastic Calculus: Class 3 — Backward equations (NYU, 2019)

    Jonathan Goodman

    brownian motion · calculus · partial differential equations · probability · stochastic calculus · stochastic processes

75. Stochastic Calculus: Class 4 — Ito integral for Brownian motion (NYU, 2019)

    Jonathan Goodman

    brownian motion · calculus · stochastic calculus · stochastic processes

76. Stochastic Calculus: Class 5 — multi-component diffusions (NYU, 2019)

    Jonathan Goodman

    calculus · probability · stochastic calculus · stochastic differential equations · stochastic processes

77. Stochastic Calculus: Class 6 — linear problems, more (NYU, 2019)

    Jonathan Goodman

    calculus · probability · stochastic calculus · stochastic differential equations · stochastic processes

78. Stochastic Calculus: Class 8 — More differential equations (NYU, 2019)

    Jonathan Goodman

    calculus · partial differential equations · probability · stochastic calculus · stochastic differential equations · stochastic processes

79. Stochastic Calculus: Class 9 — More differential equations, continued (NYU, 2019)

    Jonathan Goodman

    calculus · partial differential equations · probability · stochastic calculus · stochastic processes

80. Stochastic Calculus: Final Exam Practice (NYU, 2018)

    Jonathan Goodman

    brownian motion · calculus · martingales · probability · stochastic calculus · stochastic differential equations

81. Stochastic Calculus: Lesson 1 — Brownian motion (NYU, 2018)

    Jonathan Goodman

    brownian motion · calculus · probability · stochastic calculus · stochastic processes

82. Stochastic Calculus: Lesson 2 — Diffusion processes (NYU, 2018)

    Jonathan Goodman

    calculus · stochastic calculus · stochastic differential equations · stochastic processes

83. Stochastic Calculus: Lesson 3 — Ito integral (NYU, 2018)

    Jonathan Goodman

    probability · stochastic calculus · stochastic differential equations · stochastic processes

84. Stochastic Calculus: Lesson 4 — Ito’s lemma (NYU, 2018)

    Jonathan Goodman

    calculus · stochastic calculus · stochastic processes

85. Stochastic Calculus: Lesson 5 — SDE and PDE (NYU, 2018)

    Jonathan Goodman

    calculus · partial differential equations · probability · stochastic calculus · stochastic differential equations · stochastic processes

86. Stochastic Calculus: Lesson 6 — Simulating, change of measure (NYU, 2018)

    Jonathan Goodman

    calculus · monte carlo simulation · numerical methods · probability · stochastic calculus · stochastic differential equations

87. Stochastic Calculus: Lesson 8 — Multi-component diffusion (NYU, 2018)

    Jonathan Goodman

    calculus · partial differential equations · probability · stochastic calculus · stochastic processes

88. Stochastic Differential Equations (MIT 18.S096, Lecture 21)

    Choongbum Lee, MIT OpenCourseWare

    numerical methods · probability · stochastic calculus · stochastic differential equations · stochastic processes

89. Stochastic Processes I (MIT 18.S096, Lecture 5)

    Choongbum Lee, MIT OpenCourseWare

    probability · stochastic processes

90. Stochastic Processes II (MIT 18.S096, Lecture 17)

    Choongbum Lee, MIT OpenCourseWare

    brownian motion · probability · stochastic processes

91. Term Structure Lattice Models (Columbia IEOR E4706)

    Martin Haugh

    derivatives · financial engineering · fixed income · interest rates · martingales · mathematical finance

92. The Black-Scholes Model (Columbia IEOR E4706)

    Martin Haugh

    derivatives · financial engineering · mathematical finance · option pricing · volatility surface

93. The Fundamental Theorem Of Arbitrage Pricing (UChicago, 2001)

    Steven P. Lalley

    asset pricing · derivatives · mathematical finance · option pricing

94. The Peter Lynch Playbook

    equity analysis · fundamental analysis · growth investing · long term investing · portfolio allocation · risk reward

95. The Principles of Deep Learning Theory

    Boris Hanin, Daniel A. Roberts, Sho Yaida · 2021

    Deep Learning · Effective Theory · Facebook · MIT · Machine Learning · Neural Networks

96. Theory of Deep Learning

    SANJEEV ARORA · 2020

    Deep Learning · Machine Learning · Mathematics · Neural Networks · Theory of Deep Learning

97. Undergraduate Fundamentals of Machine Learning

    Finale Doshi-Velez, Harvard University, William J. Deuschle · 2018

    Fundamentals · Harvard · Machine Learning · Supervised & Unsupervised Learning · Undergraduate Thesis