Francesco Cesarone

Courses at University of Roma Tre
 Computational Finance (20152016)
Syllabus:
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; Elementbyelement multiplication and division; Colon (:) operator; Predefined function; inline Function; Anonymous Function.
1.2 Mfile: 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 Higherorder moments and synthetic indices of a distribution
2.5 Some probability distributions: Uniform, Normal, Lognormal, Chisquare, Studentt
3 Linear and Nonlinear Programming
3.1 Some Matlab builtin functions for optimization problems
3.2 Multiobjective optimization: Determining the efficient frontier
4 Portfolio Optimization
4.1 Portfolio of equities: Prices and returns
4.2 Riskreturn analysis: MeanVariance; Effects of the diversification in an Equally Weighted portfolio; MeanMAD; MeanMinMax; VaR; MeanCVaR; MeanGini 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; Multiperiod case
6.2 BlackScholes 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
"Where there is a will there is a way..."