Francesco Cesarone

    Courses at University of Roma Tre
  • Computational Finance (2015-2016)

    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; 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

    "Where there is a will there is a way..."