Mathematical Finance: Theory, Modeling, Implementation
Suggestions for Lecturers
In the following you find some suggestions for lectures based on the book.
The book is sufficient for two semesters, each having 14 units of 90 min lecture.
Lecture: Mathematical Finance Introduction
The lecture tries to be fully self-contained, repeating some basic material from probability theory. However, the lecture does not give many proof. Proofs are only given if they show important aspects or techniques (like the derivation of the Black-Scholes formula). Each session takes approximately 90 min.
Session 0: Introduction (optional)
Introduce the idea of replication following Section 3.1.
- Introduce the static hedge.
- Motivating the need for a stochastic model for a dynamic hedge.
- Motivate the idea of a change of measure using Section 3.1.2.
Session 1: Foundations from Probability Theory
Section 2.1 to 2.3
Session 2: Building Stochastic Processes
Section 2.4 to 2.6
Session 3: Ito Calculus, Martingales, Martingale Representation
Section 2.6.1 to 2.9
Session 4: Replication, Change of Measure
Session 5: First Application: Black-Scholes Model
Session 6: Interest Rates
Session 7: Simple Interest Rate Products
Session 8: Simple Interest Rate Options
Chapter 10: The Black Model for a Caplet
Session 9: LIBOR Market Model: Derivation of the Drift, Model Parameters
Chapter 19, Section 19.1 to 19.2
Session 10: LIBOR Market Model: Model Properties and Model Intuition
Chapter 19, Section 19.4; Chapter 25
Session 11: Discretization and Monte-Carlo Simulation
Chapter 13, Application to Black-Scholes Model and/or LIBOR Market Model
Session 12: Pricing Bermudan Option in a Monte Carlo Simulation
Section 15.1 to 15.4: Bermudan Options and the Backward Algorithm
Session 13: Pricing Bermudan Option in a Monte Carlo Simulation: Estimating the Excercise Criteria
Section 15.5 to 15.8, 15.10
Session 14: Sensitivities of Monte Carlo Prices: Problem Description
Section 17.1 to 17.3
Session 15: Sensitivities of Monte Carlo Prices: Problem Solutions
Section 17.4 to 17.8