| Computational Finance
(objectives)
The course objective is to educate students about the MATLAB language and development environment, for programming, numerical calculation and visualization applied to financial problems.
The rule of Computational Finance is becoming increasingly important in the financial industry, both for the modeling and analysis phase, as well as for the decision-making phase.
Many models used in practice are formulated via complex mathematical problems, for which an exact or a closed-form solution could not be obtained. Consequently, computational techniques and specific numerical algorithms are required to solve such cases.
Over the duration of the Course, we attempt to integrate the understanding of theoretical with their practical use. The application of quantitative financial models will be used to simplify the comprehension of some mathematical and statistical concepts and to learn the main computational techniques, which are useful to deal with a wide range of financial problems, such as portfolio optimization, risk management and derivatives pricing. Therefore, this course is not only suitable for university students, but also for professionals who want to deepen their knowledge and understanding of the quantitative financial models explored in this course.
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Derived from
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21201730 Computational Finance in Finance and business LM-16 CESARONE FRANCESCO
(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
(reference books)
F Cesarone (2020), Computational Finance. MATLAB oriented modeling, Routledge-Giappichelli Studies in Business and Management, ISBN 978-0-367-49303-5
https://www.giappichelli.it/computational-finance
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Dates of beginning and end of teaching activities
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Delivery mode
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At a distance
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Attendance
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not mandatory
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Università Roma Tre