Introduction to Probability Theory and Statistics. Probability Space, Random Variables, Expectation, Variance, Higher Moments. Random Vectors, Conditional Distributions, Regression
Introduction to MATLAB Programming. MATLAB Environment. Programming, Graphics.
Simulation of Random Processes. Simulating Discrete and Continuous Random Variables. Simulation of Random Vectors. Gaussian Process, Random Walk, Wiener Process, Brownian Bridge.
Modeling the Dynamics of Asset Prices
Binomial Models for Option Pricing. Calibrating a Binomial Lattice. Binomial and Trinomial Lattices.
Foundations of Monte Carlo Methods. Path Generation. Option Pricing. The Least Squares Method and the Dynamic Programming approach.
Credit Risk and the Valuation of Corporate Securities.
Optimization Models and Portfolio Management.
Risk Management and Value at Risk. Types of Financial Risks. Approaches to Compute Vale at Risk. Computing Value at Risk by Monte Carlo Simulations.