Francesco Cesarone

Courses

 

Courses at Roma Tre University:

 

  • FINANZA COMPUTAZIONALE (Master Degree), 2015 - present.
  • FINANCIAL MODELING (Master Degree), 2018 - present.
  • METODI MATEMATICI PER LE DECISIONI ECONOMICHE E AZIENDALI (Master Degree), 2024 - present.

 

FINANZA COMPUTAZIONALE  & FINANCIAL MODELING - Syllabus:

 

Module 1

  • A rapid introduction to MATLAB
  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
  2. M-file: Script and Function
  3. Programming fundamentals: if, else, and elseif scheme; for loops; while loops
  4. Matlab graphics
  5. Preliminary exercises on programming
  6. Exercises on the financial evaluation basics

 

Module 2

  • Preliminary elements on Probability Theory and Statistics 
  1. Random variables 
  2. Probability distributions 
  3. Continuous random variable 
  4. Higher-order moments and synthetic indices of a distribution 
  5. Some probability distributions: Uniform, Normal, Log-normal, Chi-square, Student-t
  • Linear and Non-linear Programming 
  1. Some MATLAB built-in functions for optimization problems
  2. Multi-objective optimization: Determining the efficient frontier
  • Portfolio Optimization 
  1. Portfolio of equities: Prices and returns
  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
  3. Bond portfolio immunization

 

Module 3

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

 

 

METODI MATEMATICI PER LE DECISIONI ECONOMICHE E AZIENDALI - Syllabus:

 

  • Linear Algebra and Preliminary Tools
  1. Vectors and basic operations
  2. Matrices: operations, determinants, rank, inverse
  3. Linear systems: solution methods, fundamental theorems (Cramer, Rouchè-Capelli)
  4. Eigenvalues and eigenvectors
  • Inequalities and Multivariable Functions
  1. Plane inequalities
  2. Multivariable functions: domain, continuity, differentiability
  3. Gradient, Hessian, local and global maximum/minimum (Weierstrass, Fermat theorems)
  4. Taylor expansions and approximations

 

  • Mathematical Programming
  1. Convex functions and convex sets
  2. Quadratic forms and constrained optimization
  3. Linear Programming (LP): formulation, geometry, vertices, simplex method
  4. Duality: fundamental theorems and economic interpretations
  5. Sensitivity analysis, shadow prices, transportation and assignment problems
  6. Integer Linear Programming
  7. Unimodular and totally unimodular matrices
  8. Application to real problems: capital budgeting, production, investment planning
  9. Multi-objective programming: Pareto optimality, scalarization methods
  10. Markowitz portfolio selection model
  11. Multi-attribute programming

 

  • Graph Theory and Applications
  1. Preliminary notions of graph theory
  2. Maximum flow problem
  3. PERT/CPM models and networks
  4. Travelling Salesman Problem (TSP)

 

  • Excel Laboratory