Università Roma Tre

MODULE 1
1 A rapid introduction to MATLAB
1.1 MATLAB basics: Preliminary elements; Variable assignment; Workspace; Arithmetic operations; Vectors and matrices; Standard operations of linear algebra; Element-by-element multiplication and division; Colon (:) operator; Predefined function; inline Function; Anonymous Function.
1.2 M-file: Script and Function
1.3 Programming fundamentals: if, else, and elseif scheme; for loops; while loops
1.4 Matlab graphics
1.5 Preliminary exercises on programming
1.6 Exercises on the financial evaluation basics

MODULE 2
2 Preliminary elements on Probability Theory and Statistics
2.1 Random variables
2.2 Probability distributions
2.3 Continuous random variable
2.4 Higher-order moments and synthetic indices of a distribution
2.5 Some probability distributions: Uniform, Normal, Log-normal, Chi-square, Student-t
3 Linear and Non-linear Programming
3.1 Some Matlab built-in functions for optimization problems
3.2 Multi-objective optimization: Determining the efficient frontier
4 Portfolio Optimization
4.1 Portfolio of equities: Prices and returns
4.2 Risk-return analysis: Mean-Variance; Effects of the diversification in an Equally Weighted portfolio; Mean-MAD; Mean-MinMax; VaR; Mean-CVaR; Mean-Gini portfolios
4.3 Bond portfolio immunization

MODULE 3
5 Further elements on Probability Theory and Statistics
5.1 Introduction to the Monte Carlo simulation
5.2 Stochastic processes: Brownian motion; Ito’s Lemma; Geometrical Brownian motion
6 Pricing of derivatives with an underlying security
6.1 Binomial model (CRR): A replicating portfolio of stocks and bonds; Calibration of the model; Multi-period case
6.2 Black-Scholes model: Assumptions of the model; Pricing of a European call; Pricing equation for a call; Implied Volatility
6.3 Option Pricing with Monte Carlo Method: Solution in integral form; Path Dependent Derivatives

F. Cesarone, Computational Finance: a MATLAB oriented modeling, draft