Sumários

15 Outubro 2018, 11:30 • João Guerra

Discussion of Exam Style exercises on Sde's, Ito formula and financial applications.

11 Outubro 2018, 11:30 • João Guerra

The efficient market hypothesis.

The continuous time lognormal model: advantages and drawbacks.

The constant volatility assumption and the volatility smile effect.

The normality assumption and the fat tails of the returns empirical distribution.

8 Outubro 2018, 11:30 • João Guerra

SDE's driven by Brownian motion.

The Orsnstein-Uhlenbeck process with mean reversion.

The mean reversion effect. The stationary distribution for the Orsnstein-Uhlenbeck process with mean reversion.

Financial applications: the Vasicek model and the Black-Scholes model with stochastic volatility.

4 Outubro 2018, 11:30 • João Guerra

Multidimensional Itô formula: examples of application.

Stochastic differential Equations: determinist equations and stochastic equations. How to solve them.

Examples: the stochastic differential equation of the geometric Brownian motion; the Langevin equation (Ornstein-Uhlenbeck process).

1 Outubro 2018, 11:30 • João Guerra

Calculate a stochastic integral by definition: example.

Ito formula and Ito processes: motivation and examples.

One-dimensional Ito formula: example related to finance.