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.

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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. 

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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. 

 

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Exercise. Stochastic exponentials.

15 Novembro 2018, 10:00 • João Guerra

Exercise involving Itô formula and a Gronwall lemma. 

Stochastic exponentials. 

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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. 

 

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