First part: stochastic calculus
1. Introduction to stochastic processes
Discrete processes; binomial lattices; Wiener process; filtrations; stochastic integrals; martingales; Itô’s lemma.
2. Stochastic differential equations
Introduction to ordinary differential equations (ODE); geometric Brownian motion; stochastic differential equations (SDE); Feynman-Kač and Girsanov formulae.

Second part: stochastic models for finance.
1. Stock market models
Black e Scholes model; European option pricing; risk neutral probabilities; American option pricing (basics); hedging; Greeks; smile effect; empirical evidence.
2. Interest rate models
Review of the term structure of interest rates; short rate; Vasiček model; Cox, Ingersoll e Ross (CIR) model; affine models.