Courses at Roma Tre University:
- Finanza Computazionale (Master Degree), 2015 - present.
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Financial Modeling (Master Degree), 2018 - present.
Syllabus:
MODULE 1-
A rapid introduction to MATLAB
- 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
- M-file: Script and Function
- Programming fundamentals: if, else, and elseif scheme; for loops; while loops
- Matlab graphics
- Preliminary exercises on programming
- Exercises on the financial evaluation basics
MODULE 2-
Preliminary elements on Probability Theory and Statistics
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Random variables
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Probability distributions
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Continuous random variable
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Higher-order moments and synthetic indices of a distribution
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Some probability distributions: Uniform, Normal, Log-normal, Chi-square, Student-t
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Linear and Non-linear Programming
- Some MATLAB built-in functions for optimization problems
- Multi-objective optimization: Determining the efficient frontier
- Portfolio of equities: Prices and returns
- Risk-return analysis: Mean-Variance; Effects of the diversification in an Equally Weighted portfolio; Mean-MAD; Mean-MinMax; VaR; Mean-CVaR; Mean-Gini portfolios
- Bond portfolio immunization
MODULE 3
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Further elements on Probability Theory and Statistics
- Introduction to the Monte Carlo simulation
- Stochastic processes: Brownian motion; Ito's Lemma; Geometrical Brownian motion
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Pricing of derivatives with an underlying security
- Binomial model (CRR): A replicating portfolio of stocks and bonds; Calibration of the model; Multi-period case
- Black-Scholes model: Assumptions of the model; Pricing of a European call; Pricing equation for a call; Implied Volatility
- Option Pricing with Monte Carlo Method: Solution in integral form; Path Dependent Derivatives.