Sumários

Lévy processes, Lévy measures and subordinators

25 Outubro 2022, 09:30 • João Guerra

Lévy processes and Lévy measures: examples. 

Subordinators. Examples

Exercises and Stable distributions

20 Outubro 2022, 13:30 • João Guerra

Exercises about characteristic functions, infinitely divisible distributions, Lévy measures and Cauchy distribution. 

The stable distributions and the general central limit problem. 
Properties of stable distributions. The "fat tails" property for stable distributions with \alpha <2. 

Lévy measures and Lévy-Khintchine formula

18 Outubro 2022, 09:30 • João Guerra

Lévy measures: definition and examples. 

Levy-Khintchine formula: sketch of the proof and examples. 

Introduction to Lévy processes. Characteristic Functions and Infinitely divisible distributions

13 Outubro 2022, 13:30 • João Guerra

Conclusion of the introduction to Lévy processes: the jump-diffusion characteristic function and the Lévy-Khintchine formula, some examples of Lévy processes used in asset pricing, main techniques for option pricing in Lévy models. 

Characteristic Functions: definition and main properties. Examples and exercises. 
Infinitely divisible distributions and random variables: definition and examples. 

Presentation. Introduction to Lévy processes

11 Outubro 2022, 09:30 • João Guerra

Presentation of the course. 

Weaknesses of the  Black-Scholes model and how Lévy models can help surpass these drawbacks. 
Definition of Lévy process. 
Some examples of Lévy processes.