Infinitely divisible distributions - Examples

23 Setembro 2020, 11:30 • João Guerra

Basic examples of Lévy processes used in financial applications. 

Subordinators. Basic definition and example. 

Characteristic function. Definition. Exercise. 

Infinitely divisible distributions and random variables. Examples. 

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Introduction to infinitely divisible distributions, Lévy-Khintchine formula and Lévy measures

21 Setembro 2020, 10:00 • João Guerra

Characteristic function. Definition and example for the jump-diffusion process. 

Lévy-Khintchine formula and Lévy-Itô decomposition of a Lévy process. 

Lévy measure. Example. 

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Introduction to Lévy processes

16 Setembro 2020, 11:30 • João Guerra

The imperfections of the Black-Scholes model: the implied volatility smile. 

Implied volatility: definition and how to calculate it. Example. 

Definition of Lévy process. Examples. 

The compound Poisson process and the jump-diffusion process. 

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Presentation and general introduction

14 Setembro 2020, 10:00 • João Guerra

Presentation: Programme, Bibliography and Assessment. 

General introduction to Lévy processes:  Importance of Lévy processes and main areas of application. 

The imperfections of the Black-Scholes model: presence of jumps in asset price data and the empirical distribution of log-returns (fat-tails and skewness) versus the normal distribution associated to Black-Scholes model. 

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