Ateneo - UPO

There are two modules 4 CFU each:

Module 1 – Prof. Giovanni Longo – Forward contract, term structure of interest rates, FRA, swap, bootstrapping by Nelson&Siegel model, interest rate risk management, binomial model, Black&Scholes and Black formulas, pricing of some classic derivatives and structured products.

Module 2 – Prof.ssa Francesca Centrone
The main notions and problems concerning classical Portfolio Theory (Markowitz model, CAPM, APT) are presented and discussed, and the most important result derived analitically. The main features and problems in Portfolio Theory are faced. Basic notions about Risk measures theory ad Risk Parity are also introduced. The main presented models are also implemented in Matlab.

Module 1 - Teaching material downloadable on the course web site (www.dir.uniupo.it).

Other useful books (available at the library):

J. Hull, Options, Futures and Other Derivatives, 7th ed., Pearson Prentice-Hall International, 2014, including Exercise book.
R. Jarrow e Turnbull, Derivative Securities, South Western, 1994.

Module 2
1) F. Cesarone
Computational Finance, Matlab Oriented modeling. Giappichelli Editore 2020.
2) C. Huang, R. H. Litzenberger.
Foundations for Financial Economics. Prentice Hall. 1988.
All the textbooks can be found in the Department library.
3) Material provided by the teacher on the course page on www.dir.uniupo.it

Module 1 - By the end of the couse students should be able to price and replicate forward contracts; to bootstrap the interest rate curve from market data, to price and use swaps both for curve construction and hedging instrument; to know how to boostrap the interest rate curve with the Nelson&Siegel model and to use it for measuring and hedging interest rate risk. To know how to construct a binomial model for stochastic evolution of underlying assets and to use it for pricing and hedging some classic derivatives. To know the Black&Scholes formula (as a limit of the binomial model) and to use it both for pricing and hedging. To know the Black formula for pricing some classic interest rate derivatives. To know how to decompose a structured contract and, with the skills got during the course, to price and hedge them.

Modulo 2 - By the end of the module, the student should have acquired a suitable knowledge of the quantitative tools to understand the main themes in Portfolio Theory in a critical way. The student should also have developped the right sensibility and comprehension skills to solve problems in this context.

Contents of the courses of Metodi Matematici 1, 2 and Statistics.
To know how to use Excel and the fundamentals of Matlab.

Lectures including both theory and exercises. Parts of the lectures will be run in the computer laboratory with the use of Excel and Matlab.

Attendance of the lecture class is not compulsory but is strongly recommended.
Notions of basic Decision Theory under uncertainty facilitate the understanding of the course contents.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents- physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects. When dealing with ESG aspects and the sustainability objective, the importance of good corporate governance will be highlighted in the various profiles, including gender equality.

Module 1 – Practical Exam in English
The exam will consist of solving a set of problems using Excel, followed by an oral discussion.
The structure of the exam is designed to assess the understanding of the topics covered in the course and the ability to apply the acquired knowledge to the analysis of structured problems.

At the end of the course, in the first half of December, there will be the possibility to take an informal exam. This will be a practical test with Excel, and no oral discussion will be required.

Modulo 2 - A compulsory oral exam in English, during which the student will also be asked to solve some problems on the course topics. Some problems will be of computational nature and will aim at checking the knowledge of the main formulas in Portfolio Theory. Other problems, of theoretical character, will check the comprehension and the skills to solve more complex and non standard questions.
For the interested students, there will be the possibility of sustaining a written exam at the end of the course with the same structure of the oral exam.

Note: It is compulsory to enroll in the exams via the Portale Studenti platform. Exceptions will not be accepted. Exams of the two modules are independent. They can be taken in different sessions and without having to respect any order. The exam of the single module is considered passed if the vote is not less than 15/30. If accepted on the Portale Studenti platform, it will remain valid for 2 years, otherwise it is lost. The whole exam is passed when both modules are passed and the average result of not less than 18/30 (also the result of the last module has to be accepted on the Portale Studenti ). The record of the whole exam is done by “appelli verbalizzanti” fixed at the end of each session. Also for them it is necessary to enroll through Portale Studenti , indicating in the notes the date of the passed modules (with acceptance of the votes).
There are 7 exam sessions in each solar year but students can enroll no more than three times, at their own choice. It is mandatory to register for the exam through the students portal: once the three exam participations have been reached, including withdrawals and refusals, the system will not allow further registrations.

Module 1 – Derivatives pricing

Forward contracts. Characteristics of the contract, long and short positions, replicating portfolio, with dividend, and/or costs. Value of a forward contract.
Interest rate construction from market data, FRA and Swaps. Linear interpolation and bootstrapping through Nelson&Siege. Use of the model for sensitivity analysis and hedging of interest rate instruments.
Financial options. Features of a standard contracts: call and put options, American and European. Variables that affect the price of the options. Restrictions on option prices. Modeling of the evolution of the underlying with binomial trees. Risk neutral probability. Pricing of an option with the binomial model. Delta of an option. Replicating portfolio (dynamic). The case of American options. The Black & Scholes model. Dynamic hedging. Limits of the Black-Scholes model. Some outlines to the Black model for rates, caps and floors.

Module 2 - Portfolio Theory

Random variables and optimization: refresh. Basic notions of Decision Theory under Uncertainty.
The problem of portfolio diversification and of the construction of a portfolio of risky assets. The Markowitz mean-variance problem, the efficient frontier without and with a riskless asset. Implementation with Matlab. Problems connected with the estimation of the parameters. Sharpe index and risk premium. CAPM and APT. Introduction to risk measures and risk parity.

Module 1 - By the end of the couse students should be able to price and replicate forward contracts; to bootstrap the interest rate curve from market data, to price and use swaps both for curve construction and hedging instrument; to know how to boostrap the interest rate curve with the Nelson&Siegel model and to use it for measuring and hedging interest rate risk. To know how to construct a binomial model for stochastic evolution of underlying assets and to use it for pricing and hedging some classic derivatives. To know the Black&Scholes formula (as a limit of the binomial model) and to use it both for pricing and hedging. To know the Black formula for pricing some classic interest rate derivatives. To know how to decompose a structured contract and, with the skills got during the course, to price and hedge them.
Modulo 2 - By the end of the module, the student should have acquired a suitable knowledge of the quantitative tools to understand the main themes in Portfolio Theory in a critical way. The student should also have developped the right sensibility and comprehension skills to solve problems in this context.