Sumários
Exponential martingales and option pricing
27 Novembro 2018, 10:00 • João Guerra
Parameter estimation and exotic option pricing.
No arbitrage conditions for exponential Levy processes. Exercise.
Aacsb AOL test.
Equivalent martingale measures in Lévy models
22 Novembro 2018, 10:00 • João Guerra
Equivalent martingale measures in Lévy models: characterization and examples.
Incomplete and complete markets.
Esscher transform and mean-correcting martingale measure.
Exponential martingales and option pricing
20 Novembro 2018, 10:00 • João Guerra
Martingales and exponential martingales.
The Girsanov theorem.
Option pricing problem in Lévy market models.
Fudamental theorems of asset pricing.
Complete and incomplete markets. Existence and uniqueness of equivalent martingale measures. Examples.
Exercise. Stochastic exponentials.
15 Novembro 2018, 10:00 • João Guerra
Exercise involving Itô formula and a Gronwall lemma.
Stochastic exponentials.
Lévy type stochastic integrals and Itô formula
13 Novembro 2018, 10:00 • João Guerra
Stochastic integration with respect to semimartingales and Lévy processes.
Predictable processes.
Integration of simple processes.
Integration with respect to the martingale part of Lévy processes.
Lévy type stochastic integrals.
The Itô formula.
Exercise.