Sumários

Stochastic exponential, exponential martingales, option pricing

4 Novembro 2025, 09:30 • João Guerra

Stochastic exponential. Examples.
Exponential martingales. Examples. 
Complete and incomplete markets. Arbitrage free markets. The Meta-theorem for arbitrage and completeness. Examples. 

Mean correcting martingale measure

28 Outubro 2025, 09:30 • João Guerra

Modeling stock price as the exponential of a Lévy process. 

Mean correcting martingale measure: stock price under the mean correcting martingale measure and the drift change. 
Discussion of exercises about the Itô formula. 

Itô formula

22 Outubro 2025, 14:00 • João Guerra

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

Examples. 

Stochastic integrals for jump processes. Lévy-type stochastic integrals.

21 Outubro 2025, 09:30 • João Guerra

Predictable processes and definition of stochastic integrals for jump processes and Lévy processes. 

Itô processes and Lévy-type stochastic integrals. Examples. 

Lévy-Itô decomposition

15 Outubro 2025, 14:00 • João Guerra

Finite variation functions and finite variation processes. Examples. 

When Lévy processes have finite variation. 
Finite and infinite activity processes. 
Lévy-Itô decomposition. 
The simulation of Lévy processes. 
Simulation of Brownian motion and of Poisson processes. 
The general method of simulation for Lévy processes.