Financial operations and regimes. Annuities and amortization schedules. NPV, IRR and choice criteria for investment operations. Zero coupon bonds and coupon bonds. Duration e convexity. Excel for financial applications.
Course Content - Last names M-O
Financial operations and regimes. Annuities and amortization schedules. NPV, IRR and choice criteria for investment operations. Zero coupon bonds and coupon bonds. Duration e convexity. Excel for financial applications.
Course Content - Last names P-Z
Financial operations and regimes. Annuities and amortization schedules. NPV, IRR and choice criteria for investment operations. Zero coupon bonds and coupon bonds. Duration e convexity. Excel for financial applications.
Linear algebra: handouts.
Integrals: Metodi matematici per l'analisi economica e finanziaria (Pearson, 2015). Knut Sydsaeter, Peter Hammond, Arne Strøm
Chapter 6
Goals: being able to solve linear systems, manipulate matrices, use matrix notation, compute rank and determinant.
Integrals: being able to compute antiderivatives and indefinite integrals, compute simple definite integrals and generalized integrals.
Learning Objectives - Last names F-L
To be able to formalize, in mathematical terms, basic financial problems.
To be able to apply tools from Calculus to solve them.
To be able to implement the solution process with a PC (using Excel).
To be able to verify the consistency of the obtained solutions.
Learning Objectives - Last names M-O
To be able to formalize, in mathematical terms, basic financial problems.
To be able to apply tools from Calculus to solve them.
To be able to implement the solution process with a PC (using Excel).
To be able to verify the consistency of the obtained solutions.
Learning Objectives - Last names P-Z
To be able to formalize, in mathematical terms, basic financial problems.
To be able to apply tools from Calculus to solve them.
To be able to implement the solution process with a PC (using Excel).
To be able to verify the consistency of the obtained solutions.
Prerequisites
Calculus for funcions of a single variables: limits and derivatives.
Prerequisites - Last names F-L
Matematica per le Applicazioni Economiche
Prerequisites - Last names M-O
Matematica per le Applicazioni Economiche
Prerequisites - Last names P-Z
To seat the exam there are no formal prerequisites.
Some knowledge of basic calculus of Matematica per le Applicazioni Economiche are required.
Teaching Methods
Lectures.
Teaching Methods - Last names F-L
Class lectures and exercise sessions (also using Excel).
Teaching Methods - Last names M-O
Class lectures and exercise sessions (also using Excel).
Teaching Methods - Last names P-Z
Class lectures and exercise sessions (also using Excel).
Further information
More details on moodle: https://e-l.unifi.it/course/view.php?id=11471
Further information - Last names F-L
Students are warmly invited to enrol in the Moodle page of the course (''a.y. 19-20, canale F-L''). The password to access it will be provided during the first lecture (or by email).
Further information - Last names M-O
Students are warmly invited to enrol in the Moodle page of the course (''a.y. 19-20, canale M-O''). The password to access it will be provided during the first lecture (or by email).
Further information - Last names P-Z
Students are warmly invited to enrol in the Moodle page of the course (''a.y. 19-20, canale P-Z''). The password to access it will be provided during the first lecture (or by email).
Type of Assessment
Written test.
Type of Assessment - Last names F-L
Written exam with 3 problems and a multiple-choice question on Excel. Closed book exam; a pocket calculator is allowed. See E-Learning for more details.
Type of Assessment - Last names M-O
Written exam with 3 problems and a multiple-choice question on Excel. Closed book exam; a pocket calculator is allowed. See E-Learning for more details.
Type of Assessment - Last names P-Z
The written test will take place online using the Moodle platform located at https://e-val.unifi.it.
The test will consist of a series of questions that the student can also answer in a non-sequential form (therefore it is not necessary to have answered question n-1 to answer question n). Some questions will be multiple choice, others will require a numerical answer from the student. In this case the students will have to carry out the calculations with pen and paper and with the aid of a calculator, as if the exam took place in the classroom. It is not allowed to use the PC in place of the calculator. Some questions may include the insertion of numeric results (amounts, rates, etc.) by means of a keyboard. In addition, there will be a question, always multiple choice, on the part of Excel.
The questions will be randomly drawn from a "Question Bank" and the numerical values necessary to carry out the counting will be different and personalized for each student. For questions that require a numerical answer, a tolerance is foreseen that will allow to accept as valid the answers that show modest differences with respect to the correct value.
The time for carrying out the test, after having correctly identified the students, is set at 45 minutes.
For each correct answer a score will be assigned, highlighted next to the question. The total test score is 33 points. The question about Excel will be worth 3 points. There are no penalties for wrong answers. The test result will be communicated by the teachers subsequently via the Moodle platform.
In case of doubts about the evaluation, the teacher may ask for some students to carry out an additional oral test on the whole program of the course.
See the e-Learning page for all the details.
Course program
Matrices and their operations. Linear systems. Gaussian algorithm. Rank, determinant and the Cramer's rule.
Antiderivatives and indefinite integration. Integration by parts and by substitution. Definite and generalized integrals.
Course program - Last names F-L
References are to the textbook “Matematica Finanziaria”, G. Scandolo
Basic financial operations (chap 1)
Annuities evaluation and debt amortization (chap 3)
Internal rate of returns and choice criteria for financial projects (chap 4)
Bonds, Zero Coupon Bonds and Coupon Bearing Bonds, bond yield (chap 5)
Duration and convexity (chap 7)
(note: only some sections are in the program; see E-learning for details)
Course program - Last names M-O
Basic financial operations (chap 1)
Annuities evaluation and debt amortization (chap 3)
Internal rate of returns and choice criteria for financial projects (chap 4)
Bonds, Zero Coupon Bonds and Coupon Bearing Bonds, bond yield (chap 5)
Duration and convexity (chap 7)
(note: only some sections are in the program; see E-learning for details)
CAPITOLO 1:Regimi finanziari
1.1 Contratti, titoli e operazioni finanziarie
1.2 Operazioni finanziarie elementari
1.3 Regime di interesse semplice
1.4 Regime di interesse anticipato
1.5 La capitalizzazione degli interessi
1.6 Regime esponenziale (tranne pagina 31)
1.7 Convenzioni per il calcolo dei giorni.
CAPITOLO 3: Rendite e ammortamenti
3.1 Investimenti
e finanziamenti non elementari
3.2 Valutazione di una rendita
3.3 Rendite con rate costanti
3.4 Rendite con rate in progressione geometrica
3.5 Montante di una rendita
3.6 Piani di ammortamento
3.7 Forme comuni di ammortamento
3.8 Ammortamenti a tasso variabile
CAPITOLO 4: Scelta tra operazioni certe
4.1 Rendimento per investimenti elementari (tranne paragrafo 4.1.3, 4.1.4 e 4.1.6)
4.2 Rendimento per investimenti generici
4.3 Criteri di scelta per investimenti
4.4 Criteri di scelta per finanziamenti
CAPITOLO 5: Obbligazioni
5.1 Classificazione delle obbligazioni
5.2 Obbligazioni senza cedole (tranne paragrafo 5.2.6)
5.3 Obbligazioni con cedola fissa (tranne paragrafo 5.3.4, 5.3.5 e 5.3.7)
CAPITOLO 7: Immunizzazione finanziaria
7.2 Duration di Macaulay (tranne paragrafi 7.2.5, 7.2.6, 7.2.7, 7.2.8)
7.3 Convexity di Macaulay.