Sumários

12 Maio 2023, 11:00 • João Guerra

Discussion of exam problems and exercises on stochastic differential equations, PDE's and SDE's and option pricing.

10 Maio 2023, 10:00 • João Guerra

Option pricing problems and exercises.

Review problems on Brownian motion, martingales and stochastic integrals.

5 Maio 2023, 11:00 • João Guerra

Derivation of the Black-Scholes formula for the call option using the risk neutral valuation formula.

Special topics:

1) the Stratonovich stochastic integral and its relationship with the Itô stochastic integral. Stratonovich SDE's and Ito SDE's.

2) Stopping times: definition, example and basic properties.

Discussion of exercises about pricing of contingent claims under the Black-Scholes model.

3 Maio 2023, 10:00 • João Guerra

Derivation of the Black-Scholes PDE by using no arbitrage and a replicating portfolio.

Application of the Feynman-Kac formula and the Girsanov theorem in order to obtain the risk-neutral valuation formula.

Examples and exercises on the risk neutral valuation formula.

28 Abril 2023, 11:00 • João Guerra

The Black-Scholes model assumptions.

Derivation of the Black-Scholes PDE by no arbitrage and using a portfolio with options or financial derivatives.

Exercises on Feynman-Kac formulas and Girsanov theorem.