Sumários

6 Novembro 2024, 14:00 • João Guerra

Incomplete markets. How to choose an equivalent martingale measure: the Esscher transform method and the mean-correcting martingale method.

Theorem with sufficient condition for a Lévy model to be arbitrage free. Examples.

5 Novembro 2024, 09:30 • João Guerra

Lévy models in Finance. Complete and incomplete models.

Examples

30 Outubro 2024, 14:00 • João Guerra

Itô formula for Lévy processes and lévy-type stochastic integrals. Examples and exercises.

The stochastic exponential.

Exponential martingales.

29 Outubro 2024, 09:30 • João Guerra

Brief discussion of how to calculate the implied volatility.

Stochastic integration with respect to Lévy processes.

Predictable processes and the class of adapted processes for which the stochastic integrals are well defined.

Lévy-type stochastic integrals.

Itô formula for jump processes and general Itô formula for Lévy-type stochastic integrals. Example.

23 Outubro 2024, 14:00 • João Guerra

Poisson Random measures.

Poisson Stochastic integrals. Examples.

The Lévy Ito decomposition.