MATHEMATICAL FINANCE
Syllabus
Prerequisiti
base del calcolo a della teoria della probabilità, impartiti nel corso di Matematica Generale
Prerequisites
Programma
Il corso è un'introduzione alla teoria della valutazione delle attività finanziarie. Fornisce gli
strumenti di base per valutare il rischio di un portafoglio il cui valore è influenzato dalla
variazione dei tassi di interesse. Si occupa anche di flussi di cassa casuali con un
approccio media-varianza. Copre i seguenti argomenti:
Flussi di flussi di cassa deterministici
1. La teoria di base dell'interesse
2. Titoli a reddito fisso
3. La struttura per scadenza dei tassi di interesse
4. Prezzi forward e futures
4. Duration e immunizzazione
5. Teoria del portafoglio media-varianza
Program
The course is an introduction to the theory of valuation of financial assets. It provides the
basic tools for evaluating the risk of a portfolio whose value is affected by variation of
interest rates. It also deals with random cash flows with a mean-variance approach. It
covers the following topics:
Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
4. Forward and futures prices
4. Duration and Immunization
5. Mean-Variance Portfolio Theory
Testi Adottati
Books
Bibliografia
Bibliography
Modalità di svolgimento
Le lezioni consistono nell'illustrazione da parte del docente dei principali argomenti. Dopo
l'analisi teorica di ogni argomento faranno seguito delle esercitazioni pratica.
Teaching methods
of the lecture is devoted to practical examples.
Regolamento Esame
I problemi verranno assegnati settimanalmente per permettere una valutazione in itinere che contribuirà alla valutazione finale.
Sarà comunque consentito l’accesso all’esame finale anche a coloro che non partecipino alla valutazione in itienere.
L’esame finale sarà scritto e conterrà problemi di carattere pratica e teorico.
Nei problemi di tipo pratico si valuterà la capacità di applicare la conoscenza.
Nei quesiti teorici si valuteranno le capacità espositive.
Exam Rules
Problems will be assigned weekly to allow for ongoing assessment that will contribute to the final grade.
Access to the final exam will be permitted even for those who do not participate in the ongoing assessment.
The final exam will be written and will include both practical and theoretical problems.
Practical problems will assess the ability to apply knowledge.
Theoretical questions will assess presentation skills.
Modalità di frequenza
Attendance Rules
Obiettivi Formativi
disponibile in futuro, determinare il rendimento di un investimento, utilizzare la teoria dei tassi di interesse composti per costruire e valutare uno schema di rimborso come un mutuo o un sinking fund. Gli studenti impareranno la struttura a termine dei tassi di interesse, come usarla e costruirla (bootstrap). Conosceranno le caratteristiche principali dei più importanti strumenti a reddito fisso come obbligazioni, swap, futures e forward. Il corso si concluderà con una presentazione della teoria del portafoglio in un contesto di media-varianza. Al termine del corso ci si aspetta che lo studente risolva problemi tratti da situazioni di vita reale (spesso semplificate) e conosca la teoria che motiva le soluzioni pratiche.
Learning Objectives
flow available in the future, to determine the yield of an investment, to use the theory of compound interest rates to construct and a evaluate a reimbursement scheme like a
mortgage or a sinking fund. Students will learn about the term structure of interest rates, how to use it and construct it (bootstrap). They will know the main features of the most
important fixed income instruments such as bonds, swaps, futures and forward. The course will end with a presentation of the portfolio theory in mean-variance setting.
Upon completion of the course a student is expected to solve problems taken from real life situations (often simplified), and to know the theory motivating the practical solutions.
Prerequisiti
Prerequisites
Programma
strumenti di base per valutare il rischio di un portafoglio il cui valore è influenzato dalla
variazione dei tassi di interesse. Si occupa anche di flussi di cassa casuali con un
approccio media-varianza. Copre i seguenti argomenti:
Flussi di flussi di cassa deterministici
1. La teoria di base dell'interesse
2. Titoli a reddito fisso
3. La struttura per scadenza dei tassi di interesse
4. Prezzi forward e futures
4. Duration e immunizzazione
5. Teoria del portafoglio media-varianza
Program
basic tools for evaluating the risk of a portfolio whose value is affected by variation of
interest rates. It also deals with random cash flows with a mean-variance approach. It
covers the following topics:
Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
4. Forward and futures prices
4. Duration and Immunization
5. Mean-Variance Portfolio Theory
Testi Adottati
Books
Bibliografia
Bibliography
Modalità di svolgimento
Teaching methods
Regolamento Esame
I problemi verranno assegnati settimanalmente per permettere una valutazione in itinere che contribuirà alla valutazione finale.
Sarà comunque consentito l’accesso all’esame finale anche a coloro che non partecipino alla valutazione in itienere.
L’esame finale sarà scritto e conterrà problemi di carattere pratica e teorico.
Nei problemi di tipo pratico si valuterà la capacità di applicare la conoscenza.
Nei quesiti teorici si valuteranno le capacità espositive.
Exam Rules
Problems will be assigned weekly to allow for ongoing assessment that will contribute to the final grade.
Access to the final exam will be permitted even for those who do not participate in the ongoing assessment.
The final exam will be written and will include both practical and theoretical problems.
Practical problems will assess the ability to apply knowledge.
Theoretical questions will assess presentation skills.
Modalità di frequenza
Attendance Rules
Presence in the classroom of the lesson
Obiettivi Formativi
disponibile in futuro, determinare il rendimento di un investimento, utilizzare la teoria dei tassi di interesse composti per costruire e valutare uno schema di rimborso come un mutuo o un sinking fund. Gli studenti impareranno la struttura a termine dei tassi di interesse, come usarla e costruirla (bootstrap). Conosceranno le caratteristiche principali dei più importanti strumenti a reddito fisso come obbligazioni, swap, futures e forward. Il corso si concluderà con una presentazione della teoria del portafoglio in un contesto di mediavarianza. Al termine del corso ci si aspetta che lo studente risolva problemi tratti da situazioni di vita
reale (spesso semplificate) e conosca la teoria che motiva le soluzioni pratiche.
Learning Objectives
flow available in the future, to determine the yield of an investment, to use the theory of compound interest rates to construct and a evaluate a reimbursement scheme like a
mortgage or a sinking fund. Students will learn about the term structure of interest rates, how to use it and construct it (bootstrap). They will know the main features of the most
important fixed income instruments such as bonds, swaps, futures and forward. The course will end with a presentation of the portfolio theory in mean-variance setting.
Upon completion of the course a student is expected to solve problems taken from real life situations (often simplified), and to know the theory motivating the practical solutions.
Prerequisiti
Prerequisites
Programma
Flussi di flussi di cassa deterministici
1. La teoria di base dell'interesse
2. Titoli a reddito fisso
3. La struttura per scadenza dei tassi di interesse
4. Prezzi forward e futures
4. Duration e immunizzazione
5. Teoria del portafoglio media-varianza
Program
Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
4. Forward and futures prices
4. Duration and Immunization
5. Mean-Variance Portfolio Theory
Testi Adottati
Books
Modalità di svolgimento
Teaching methods
Regolamento Esame
Ci saranno compiti settimanali durante il corso. Al termine del corso è previsto un esame finale, che sarà sia scritto che orale.
Exam Rules
There will be weekly assignments during the course. At the end of the course there will be a final exam, which will be both written and oral.
Modalità di frequenza
Attendance Rules
Obiettivi Formativi
disponibile in futuro, determinare il rendimento di un investimento, utilizzare la teoria dei tassi di interesse composti per costruire e valutare uno schema di rimborso come un mutuo o un sinking fund. Gli studenti impareranno la struttura a termine dei tassi di interesse, come usarla e costruirla (bootstrap). Conosceranno le caratteristiche principali dei più importanti strumenti a reddito fisso come obbligazioni, swap, futures e forward. Il corso si concluderà con una presentazione della teoria del portafoglio in un contesto di media-varianza. Al termine del corso ci si aspetta che lo studente risolva problemi tratti da situazioni di vita reale (spesso semplificate) e conosca la teoria che motiva le soluzioni pratiche.
Learning Objectives
flow available in the future, to determine the yield of an investment, to use the theory of compound interest rates to construct and a evaluate a reimbursement scheme like a
mortgage or a sinking fund. Students will learn about the term structure of interest rates, how to use it and construct it (bootstrap). They will know the main features of the most
important fixed income instruments such as bonds, swaps, futures and forward. The course will end with a presentation of the portfolio theory in mean-variance setting.
Upon completion of the course a student is expected to solve problems taken from real life situations (often simplified), and to know the theory motivating the practical solutions.
Prerequisiti
Prerequisites
Programma
Flussi di flussi di cassa deterministici
1. La teoria di base dell'interesse
2. Titoli a reddito fisso
3. La struttura per scadenza dei tassi di interesse
4. Prezzi forward e futures
4. Duration e immunizzazione
5. Teoria del portafoglio media-varianza
Program
Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
4. Forward and futures prices
4. Duration and Immunization
5. Mean-Variance Portfolio Theory
Testi Adottati
Books
Modalità di svolgimento
Teaching methods
Regolamento Esame
Ci saranno compiti settimanali durante il corso. Al termine del corso è previsto un esame finale, che sarà sia scritto che orale.
Exam Rules
There will be weekly assignments during the course. At the end of the course there will be a final exam, which will be both written and oral.
Modalità di frequenza
Attendance Rules
Aggiornato A.A. 2022-2023
Mathematical Finance
Prof. Stefano Herzel
University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics
• Deterministic Payoffs
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Payoffs
1. Mean-Variance Portfolio Theory
2. The Capital Asset Pricing Model
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .
The bonus points will be added to the grade of the final exam.
Bonus points will be valid only until the end of the Winter exam session.
Aggiornato A.A. 2022-2023
Mathematical Finance
Prof. Stefano Herzel
University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics
• Deterministic Payoffs
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Payoffs
1. Mean-Variance Portfolio Theory
2. The Capital Asset Pricing Model
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .
The bonus points will be added to the grade of the final exam.
Bonus points will be valid only until the end of the Winter exam session.
Aggiornato A.A. 2021-2022
Mathematical Finance
Prof. Stefano Herzel
University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics
• Deterministic Payoffs
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Payoffs
1. Mean-Variance Portfolio Theory
2. The Capital Asset Pricing Model
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .
The bonus points will be added to the grade of the final exam.
Bonus points will be valid only until the end of the Winter exam session.
Aggiornato A.A. 2021-2022
Mathematical Finance
Prof. Stefano Herzel
University of Rome - Tor Vergata Business Administration and Economics Fall Semester 2021
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic and random payoffs, covering the following topics
• Deterministic Payoffs
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Payoffs
1. Mean-Variance Portfolio Theory
2. The Capital Asset Pricing Model
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013) (Chapters 1-7)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (max. 6 bonus points) and a final exam (written and oral) .
The bonus points will be added to the grade of the final exam.
Bonus points will be valid only until the end of the Winter exam session.
Aggiornato A.A. 2019-2020
B.S. in Business Administration and Economics University of Rome Tor Vergata
Fall 2018
Mathematical Finance
Stefano Herzel
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.
It covers the following topics:
• Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Cash Flows
1. Mean-Variance Portfolio Theory
2. Utility Functions and Risk Aversion
• A micro-approach to Asset Pricing
1. Investor’s preferences and prices
2. Investor’s beliefs and prices
3. Asset Pricing in incomplete Markets
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (20%) and a final exam (80%).
Aggiornato A.A. 2019-2020
B.S. in Business Administration and Economics University of Rome Tor Vergata
Fall 2018
Mathematical Finance
Stefano Herzel
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.
It covers the following topics:
• Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Cash Flows
1. Mean-Variance Portfolio Theory
2. Utility Functions and Risk Aversion
• A micro-approach to Asset Pricing
1. Investor’s preferences and prices
2. Investor’s beliefs and prices
3. Asset Pricing in incomplete Markets
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (20%) and a final exam (80%).
Aggiornato A.A. 2018-2019
B.S. in Business Administration and Economics University of Rome Tor Vergata
Fall 2018
Mathematical Finance
Stefano Herzel
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.
It covers the following topics:
• Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Cash Flows
1. Mean-Variance Portfolio Theory
2. Utility Functions and Risk Aversion
• A micro-approach to Asset Pricing
1. Investor’s preferences and prices
2. Investor’s beliefs and prices
3. Asset Pricing in incomplete Markets
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (20%) and a final exam (80%).
Aggiornato A.A. 2018-2019
B.S. in Business Administration and Economics University of Rome Tor Vergata
Fall 2018
Mathematical Finance
Stefano Herzel
Course Description
The course is an introduction to the theory of valuation of financial assets. It provides the basic tools for evaluating deterministic cash flows and random cash flows with a mean-variance approach and to the modeling of decisions through the optimization of a utility function.
It covers the following topics:
• Deterministic Cash Flow Streams
1. The Basic Theory of Interest
2. Fixed Income Securities
3. The term structure of interest rates
• Random Cash Flows
1. Mean-Variance Portfolio Theory
2. Utility Functions and Risk Aversion
• A micro-approach to Asset Pricing
1. Investor’s preferences and prices
2. Investor’s beliefs and prices
3. Asset Pricing in incomplete Markets
Textbook
David G. Luenberger, ”Investment Science” , Oxford University Press (2013)
Prerequisites
Basic knowledge of Mathematics and Statistics.
Evaluation
The final grade will be determined by class participation and homework (20%) and a final exam (80%).