Sumários

Bounds on option prices and put-call parity

18 Outubro 2023, 14:30 • João Guerra

Lower and upper bounds for European and American option prices.

Why an American call option on a stock with no dividends should not be exercised before maturity.

Put-Call parity relationship.

Forward Contracts

17 Outubro 2023, 11:30 • João Guerra

How the different factors affect options prices: Stock price, Strike price, maturity, interest rates, volatility and dividend rate. Forward Contracts: definition and how to price forward and futures contracts.

Exercises and Introduction to Financial Derivatives

13 Outubro 2023, 11:30 • João Guerra

Exercises on Stochastic Differential Equations and Itô formula.

Introduction to options and financial derivatives.

Stochastic Differential Equations

10 Outubro 2023, 11:30 • João Guerra

Stochastic Differential Equations: the Langevin Equation and the SDE for the Ornstein-Uhlenbeck process with mean reversion.

Financial applications: Vasicek model and stochastic volatility model.

Existence and uniqueness of solutions for SDE's: sufficent conditions (linear growth property and Lipschitz condition).

Example of "explosion" of differential equation.

Multidimensional Itô formula. Introduction to stochastic differential equations

3 Outubro 2023, 11:30 • João Guerra

Multidimensional Itô process.

Multidimensional Itô formula. Examples.

Exercise about the application of Itô formula.

Stochastic differential equations: solving the geometric Brownian motion SDE.