Lectures on Numerical Methods, Mathematical Finance and Computational Finance

Some of my lectures are available as videos. Addition material (code) is available via Git repositories. The lectures were recorded live with minimal post-processing (removing questions from the audience, long pauses or obvious mistakes). There are still some obvious mistakes (and maybe some not-so-obvious ones) in there, but I tried my best. For some sessions, there are multiple versions. The later version often contains updates or corrections, but the previous version sometimes has additional parts that were left out in the later version. And sometimes, the old session was a bit better than the newer one - depending on my fitness on the day of the recording.

Numerical Method (Computational Finance I)

Lecture Videos

Introduction

Session 1: Aim of the Lecture / Motivation https://youtu.be/7dQ-qmBh9OI

Computer Arithmetic

Session 2: Computer Arithmetic (1/4): Integers https://youtu.be/bNQ0ezS9dsg
Session 3: Computer Arithmetic (2/4): Floating Point Numbers (1/3): Definition https://youtu.be/ljtt7rIUehA
Session 4: Computer Arithmetic (3/4): Floating Point Numbers (2/3): Floating Point Arithmetic https://youtu.be/N_eFw8MHUcw
Session 5: Computer Arithmetic (4/4): Floating Point Numbers (3/3): Summation https://youtu.be/azCWYOJ0IZ8

Monte-Carlo Method

Session 6: Monte-Carlo Method 1: Introduction and Intuition https://youtu.be/aLzqYhEXIeo
Session 7: Monte-Carlo Method 2: Convergence Results https://youtu.be/jUsoR5h0r1w
Session 8: Monte-Carlo Method 3: Monte-Carlo Integration 1 https://youtu.be/wjRscBNWOO8
Session 9: Monte-Carlo Method 4: Monte-Carlo Integration 2 https://youtu.be/3VfhyvOOa90
Session 10: Monte-Carlo Method 4: Monte-Carlo Integration 2 https://youtu.be/cGN5ch5fFi8

Random Number Generation

Session 11: Random Number Generation 1: Pseudo Random Numbers https://youtu.be/hGJVwKOUtyY
Session 12: Random Number Generation 2: Discrepancy & Koksma-Hlawka Inequality https://youtu.be/yIoxgFK6-No
Session 13: Random Number Generation 3: Low Discrepancy Sequences (1D) https://youtu.be/S126gKlKij8
Session 14: Random Number Generation 4: Low Discrepancy Sequences (Multi-Dimensional) https://youtu.be/mcgbUTlus9Y
Session 15: Random Number Generation 5: Generating Other Distributions 1 https://youtu.be/FkGm3pUlCQM
Session 16: Random Number Generation 6: Generating Other Distributions 2 https://youtu.be/KBfkX4jbL5Y
Session 17: Random Number Generation 7: Generating Other Distributions 3: Acceptance-Rejection Method 1 https://youtu.be/frzhoCKysU4
Session 18: Random Number Generation 8: Generating Other Distributions 4: Acceptance-Rejection Method 2 https://youtu.be/5VRf8SdtC8Y
Session 19: From Acceptance-Rejection Sampling to Weighted Monte-Carlo https://youtu.be/V7AIvtay1og

Monte-Carlo Simulation of Stochastic Processes

Session 20: Monte-Carlo Simulation of Stochastic Processes https://youtu.be/64No8AsLbDA

Time Discretization of Stochastic Processes

Session 21: Time Discretization of Stochastic Processes 1 https://youtu.be/3D4OBt47v2M
Session 22: Time Discretization of Stochastic Processes 2 https://youtu.be/9NbSWalrAI0
Session 23: Time Discretization of Stochastic Processes 3: Convergence 1 https://youtu.be/rs2Bcoj-Ks0
Session 24: Time Discretization of Stochastic Processes 4: Convergence 2 https://youtu.be/lGodfjD4Aj4

Implementation

Session 25: Implementation 1/2 https://youtu.be/XTnNHaxFb3s
Session 26: Implementation 2/2 https://youtu.be/TQm-oBzTD3k

Monte-Carlo Variance Reduction

Session 27: Monte-Carlo Control Variates https://youtu.be/xgp18udRMxA

Numerical Approximation of Partial Derivatives

Session 28: Numerical Approximation of Partial Derivatives 1/2 https://youtu.be/Nsb_f-872u0
Session 29: Numerical Approximation of Partial Derivatives 2/2 https://youtu.be/v4AL7zMaO50

Excusus: Analysing Models

Session 30: Excursus: Density of the Underlying of European Options https://youtu.be/srHExGBnBS8
Session 31: Excursus: Stochastic, Local and Implied Volatility https://youtu.be/TSKiymTcm7k

Excusus: Software Development Tools

Session 32: Excursus: Software Development Tools https://youtu.be/aWGDD7IAl4o

Coding Exercises / Assignments

An important part of the lecture are coding assignments. These assignments feature autograding using automated unit tests

Related to Computer Arithmetics

Coding Assignment: Robust solution of Quadratic Equation

This is just a warm up to make you familiar with the assignments.

Coding Assignment: Summation

This is just a warm up to make you familiar with the assignments.

github.com/qntlb/numerical-methods-summation-exercise

Related to Monte-Carlo Method

Coding Assignment: Monte-Carlo Integration

In this assignment you should implement a multi-dimensional integration rule using a) the Monte-Carlo method and b) the Simpson's rule.

github.com/qntlb/numerical-methods-montecarlointegration-exercise

Coding Assignment: Control Variate

In this assignment you should implement a Monte-Carlo valuation of an Asian option, using variance reduction via a Control Variate, assuming a Black-Scholes models.

A control variate is model-dependent, so this Monte-Carlo valuation will lose its genericallity. This is a big disadvantage.

github.com/qntlb/numerical-methods-controlvariate-exercise

Other Resources

Please send feedback or questions to email@christian-fries.de - thank you.