20410438 - MF410 - Computational Finance

Basic knowledge of financial markets, introduction to computational and theoretical models for quantitative finance, portoflio optimization, risk analysis. The computational aspects are mostly developed within the Matlab environment.

CESARONE FRANCESCO

teacher profile | teaching materials

Fruizione: 21201730 FINANZA COMPUTAZIONALE in Finanza e impresa LM-16 CESARONE FRANCESCO

Programme

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

Core Documentation

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

Type of delivery of the course

The lessons will be in-person and will also be streamed on Microsoft Teams. - Team link: https://teams.microsoft.com/l/team/19%3aqyJxck95uxybTZqROCExCmIibYxPO4kyrAojrAj6Qbg1%40thread.tacv2/conversations?groupId=96a3be25-ecca-48c8-9e9b-9f7de8b08119&tenantId=ffb4df68-f464-458c-a546-00fb3af66f6a - Team code: aqqm841 The lessons will be held according to the following schedule: Tuesday 10:30-12:30 Wednesday 10:30-12:30 Thursday 15:00-17:00 We will use the following tools: - slides; - in-person and streaming lesson with direct interaction via voice and chat; - digital blackboard; - live programming on Matlab (https://www.uniroma3.it/servizi/software-in-convenzione/mathworks-campus/);​ - Professor's textbook: http://host.uniroma3.it/docenti/cesarone/Books.htm.

Type of evaluation

The exam is composed of a written and an oral part. The written part consists of the implementation on Matlab of three exercises, one for each module. The oral part covers all the topics of the program and can include both theory questions and exercises. Students who have scored no less than 16/30 on the written test are admitted to the oral exam. Students who have obtained a score that is no less than 18/30 could avoid the oral exam and obtain a score corresponding to that of the written test but with an upper limit of 24/30 (in the case of a vote in the written part that is greater than or equal to 24/30). To aspire to a higher score, the oral exam is mandatory.

CESARONE FRANCESCO

teacher profile | teaching materials

Fruizione: 21201730 FINANZA COMPUTAZIONALE in Finanza e impresa LM-16 CESARONE FRANCESCO

Programme

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

Core Documentation

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

Type of delivery of the course

The lessons will be in-person and will also be streamed on Microsoft Teams. - Team link: https://teams.microsoft.com/l/team/19%3aqyJxck95uxybTZqROCExCmIibYxPO4kyrAojrAj6Qbg1%40thread.tacv2/conversations?groupId=96a3be25-ecca-48c8-9e9b-9f7de8b08119&tenantId=ffb4df68-f464-458c-a546-00fb3af66f6a - Team code: aqqm841 The lessons will be held according to the following schedule: Tuesday 10:30-12:30 Wednesday 10:30-12:30 Thursday 15:00-17:00 We will use the following tools: - slides; - in-person and streaming lesson with direct interaction via voice and chat; - digital blackboard; - live programming on Matlab (https://www.uniroma3.it/servizi/software-in-convenzione/mathworks-campus/);​ - Professor's textbook: http://host.uniroma3.it/docenti/cesarone/Books.htm.

Type of evaluation

The exam is composed of a written and an oral part. The written part consists of the implementation on Matlab of three exercises, one for each module. The oral part covers all the topics of the program and can include both theory questions and exercises. Students who have scored no less than 16/30 on the written test are admitted to the oral exam. Students who have obtained a score that is no less than 18/30 could avoid the oral exam and obtain a score corresponding to that of the written test but with an upper limit of 24/30 (in the case of a vote in the written part that is greater than or equal to 24/30). To aspire to a higher score, the oral exam is mandatory.