Ateneo - UPO

Derivatives Pricing Module (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.

Portfolio Theory Module (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.

Derivatives Pricing Module 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, 11th ed., Pearson Prentice-Hall International, 2021, including Exercise book.; R. Jarrow e Turnbull, Derivative Securities, South Western, Second Edition 2000.Portfolio Theory Module F. Cesarone, Computational Finance, Matlab Oriented modeling. Giappichelli Editore 2020. C. Huang, R. H. Litzenberger Foundations for Financial Economics. Prentice Hall. 1988. (Optional)Material provided by the teacher on the course page on www.dir.uniupo.it

Derivatives Pricing Module(4 ECTS, 30 hours) - 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.

Portfolio Theory Module (4 ECTS, 30 hours. Teaching activities are divided into approximately 20 hours of Lectures (DE) and 10 hours of Supplementary Teaching Activities (DI))
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 developed the right sensibility and comprehension and applicative skills to solve problems in this context.

Contents of the courses Mathematical Methods 1 and 2 (real-valued functions of a real variable, differential calculus, optimization, integrals, linear algebra, financial mathematics), Statistics and basic Probability Theory.
Basic use of Excel and Matlab.

Lectures covering both theory and exercises.
Lectures are aimed at presenting the topics in the syllabus (knowledge) and their critical discussion, adopting an integrated approach that combines expository and interactive teaching. The course alternates between moments of theoretical exposition, preceded by motivational examples, and practical exercises aimed at applying the concepts introduced. For each topic, exercises and questions are proposed whose solutions and answers are discussed collectively in class in order to stimulate contributions and engagement from all students. Part of the lectures will be held in a computer lab using Excel and Matlab.

Attendance of the lecture class is not compulsory but is strongly recommended.
Notions of basic Decision Theory under Uncertainty and Applied Statistics 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.

Derivatives Pricing Module – Practical exam in English. Students will be required to solve a number of problems on a computer. An oral examination is required to confirm passing grades.
The exam structure is designed to assess the knowing and understanding of the topics presented during the module, the ability to apply the knowledge acquired to analyze and solve a set of structured problems and the ability to make independent judgments in choosing the tools to use.
In the first half of December, at the end of the course, a preliminary exam session will be held in which no oral examination is required.

Portfolio Theory Module – Oral exam during which students will be asked to work through the solution of exercises of both a computational and theoretical nature. The computational exercises (four short exercises worth a maximum of 4/30 each, and one structured exercise worth a maximum of 8/30) are designed to assess:

-knowledge and understanding of the main formulas of Portfolio Theory
-ability to apply knowledge and understanding to solve standard Portfolio Theory problems
-independent judgement in selecting the most appropriate tools for solving such problems.

The theoretical exercises will test understanding of the proofs presented during the course and the ability to solve more complex and non-standard problems. The ability to communicate clearly and rigorously the logical-deductive reasoning followed in tackling the problems will be assessed.
Learning skills are assessed through the ability to independently use the reference texts and other resources provided.

For attending students, there will be the opportunity to sit a written exam at the end of the course, with the same structure as the oral exam. Completing only the computational exercises allows a maximum grade of 24/30 to be achieved.

Exam registration through the student portal is compulsory. Once the maximum number of sittings allowed under the Academic Regulations has been reached, the system will not permit further registrations.

The exams for the two modules may be taken independently, in different sessions and in any order. A single module exam is passed with a grade of at least 15/30; the grade must be accepted on the Student Portal. If accepted, it will remain valid for the entire duration of the degree programme; if declined, it will be considered rejected and will be forfeited.
The overall exam is passed if the average of the grades obtained in the two modules is at least 18/30. The final grade will then be decided collectively by the examining board and will not necessarily be determined by the arithmetic average of the two module grades, as other elements will also be taken into account, including overall participation in the course and the student's ability to draw connections between the contents of the two modules.
The final grade may be recorded upon registration for one of the grade recording sessions scheduled at the end of each exam session on the Student Portal. Registration for the grade recording session is required, indicating in the notes field the dates on which each module exam was passed.

Derivatives Pricing Module

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.

Portfolio Theory Module

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.

Derivatives Pricing Module - By the end of the course 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.

Portfolio Theory Module – By the end of the module, students will be expected to have acquired adequate knowledge of the main Portfolio Theory models, together with the quantitative tools needed for a critical understanding of those models. Students will also be expected to have developed the tools, sensitivity and comprehension skills required to solve both theoretical and practical problems in this context. In particular, the following competences are to be acquired:

-knowledge and understanding of the main formulas of Portfolio Theory.
-ability to apply knowledge and understanding to solve standard Portfolio Theory problems.
-independent judgement in selecting the most appropriate tools for solving such problems.
-ability to communicate clearly and rigorously the logical-deductive reasoning followed in tackling the problems.
learning skills through the ability to independently use the reference texts and other resources provided.