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Computational Finance 1

Prof. Sourish Das and Prof. Bikramaditya Datta · Chennai Mathematical Institute

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About

This course introduces the fundamental concepts of Computational Finance through an integrated approach involving finance theory, mathematical techniques, and programming. Students will explore topics such as pricing bonds and options, portfolio optimization, and the Black-Scholes model. Each week connects financial applications with core mathematical tools like linear algebra, numerical methods, and probability. Programming concepts and algorithms support practical understanding and help develop computational skills for solving real-world finance problems.

Intended audience: Advanced Undergraduate / Postgraduate of Statistics, Finance, Economics, Engineering

Prerequisites: One course each in (1) probability and statistics, and (2) basic programming.

Lectures

Week 1

  1. A Tour of Computational Finance YouTube
  2. Algorithms and Computations YouTube
  3. Rates, Compounding & Interpolation YouTube
  4. Taylor Expansions YouTube
  5. Numerical Errors and Ill-Conditioning YouTube
  6. Portfolio Choice YouTube
  7. Workout problems 1 YouTube
  8. Workout problems 2 YouTube
  9. Hands-on with R week 1 YouTube
  10. Hands-on with Python week 1 YouTube

Week 2

  1. Linear Algebra Computationally YouTube
  2. Variance, Covariance, and the Matrix YouTube
  3. Choosing Weights to Hit a Target and Ill Conditioning YouTube
  4. The Shape of Risk: Eigenvalues YouTube
  5. CAPM and Factor Models as Showcases YouTube
  6. worked out problems YouTube
  7. Hands-on with R week 2 YouTube
  8. Hands-on with Python week 2 YouTube

Week 3

  1. Options, and Functions YouTube
  2. Payoffs at Expiration YouTube
  3. Functions in Three Senses YouTube
  4. A First Option Price YouTube
  5. The Lattice Extends YouTube
  6. A Note on Exotic Options YouTube
  7. Worked Out Problems YouTube
  8. Hands-on with R week 3 YouTube
  9. Hands-on with Python week 3 YouTube

Week 4

  1. Non-Linear Equations in Finance YouTube
  2. The Implied-Volatility Surface YouTube
  3. Newton's Method: Faster When It Works YouTube
  4. The Secant Method YouTube
  5. Building the Curve and the Surface YouTube
  6. Worked Out Problems YouTube
  7. Hands-on with R week 4 YouTube
  8. Hands-on with Python week 4 YouTube

Week 5

  1. Computational Calculus of Bond and Portfolio | Numerical Differentiation YouTube
  2. Duration and Convexity | Clean and Dirty Price YouTube
  3. Portfolio's Objective Function YouTube
  4. Trapezoidal and Simpson's Rule YouTube
  5. Choice under Uncertainty | Expected Utility and more YouTube
  6. Worked Out Problems 1 YouTube
  7. Worked Out Problems 2 YouTube
  8. Hands-on with R week 5 YouTube
  9. Hands-on with Python week 5 YouTube

Week 6

  1. Computational Aspects of Black Scholes YouTube
  2. Geometrix Brownian Motion YouTube
  3. PDE with American Options YouTube
  4. American Options YouTube
  5. Worked Out Problems 1 YouTube
  6. Worked Out Problems 2 YouTube
  7. Pricing Options with R; Binomial, GBM, PDE YouTube
  8. Pricing Options with Python; Binomial, GBM, PDE YouTube

Week 7

  1. Constrained Optiomisation and Arbitrage Detection YouTube
  2. Equality Constrained Markowitz YouTube
  3. The Efficient Frontier | Capital Market Line YouTube
  4. Inequality Constraint; KKT Conditions YouTube
  5. Arbitrage Detection by Linear Programming YouTube
  6. Optimization Tutorial 1 YouTube
  7. Optimization Tutorial 2 YouTube
  8. Optimization Tutorial 3 YouTube
  9. Worked Out Problems 1 YouTube
  10. Worked Out Problems 2 YouTube
  11. Markowitz Portfolio Optimization and Arbitrage Detection using R YouTube
  12. Markowitz Portfolio Optimization and Arbitrage Detection using Python YouTube

Week 8

  1. Pricing Options and Portfolio using Monte Carlo YouTube
  2. From Random Walk to Geometric Brownian Motion YouTube
  3. Sampling from Distribution; Monte Carlo Simulator YouTube
  4. European Call by Monte Carlo YouTube
  5. Expected Utility under parameter Uncertainty YouTube
  6. Beginning from the END YouTube
  7. Worked Out Problems 1 YouTube
  8. Worked Out Problems 2 YouTube
  9. Worked Out Problems 3 YouTube
  10. Monte Carlo Simulation, GBM, Pricing Asian Call using R and Colab YouTube
  11. Monte Carlo Simulation, GBM, Pricing Asian Call using Python and Colab YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
Chennai Mathematical Institute
Department
Economics
Taught by
Prof. Sourish Das, Prof. Bikramaditya Datta
Level
Undergraduate
Language
English
Subjects
Economics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge. Coordinated by IIT Madras.
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