
Course unit
FINANCIAL MATHEMATICS
SCP4063747, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2016/17
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
SECSS/06 
Mathematics for Economics, Actuarial Studies and Finance 
9.0 
Course unit organization
Period 
Second semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
9.0 
64 
161.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
3 Commissione a.a.2018/19 
01/10/2018 
30/09/2019 
MAGRIS
ADILA
(Presidente)
CESARONI
ANNALISA
(Membro Effettivo)
GROSSET
LUCA
(Membro Effettivo)

2 Commissione a.a.2017/18 
01/10/2017 
30/10/2018 
MAGRIS
ADILA
(Presidente)
CESARONI
ANNALISA
(Membro Effettivo)
FERRANTE
MARCO
(Membro Effettivo)
GROSSET
LUCA
(Membro Effettivo)

Prerequisites:

Properties of continuous and derivable functions, sequences and series, linear algebra. 
Target skills and knowledge:

at the end of the course students will know:
1. Simple interest rate, compound interest rate, accumulation factor, compound interests, annuities: net present value and future value in the case of constant installments, perpetuities, annuityimmediate, annuitydue. Amortization schedules: principal, interest, principal repayment, balance. Choice between financial operations: Net Present Value criterion, Interest Rate of Return criterion.
2. Bonds: zero coupon bonds: face value, maturity date, simple/compound return, trading return, taxation. Coupon bonds, coupon rate, yield to maturity, dirty price, clean price, accrued interest, issuance price, risk of default.
3. Term structure: yield curve, rate curve: coupon bonds like zero coupon bonds portfolio, unitary price structure; complete and incomplete markets: superfluous bonds, noarbitrage price.
4. Macaulay duration, its properties, portfolio duration, bond duration; Macaulay convexity, efficient portfolio, assets and liabilities, Redington theorem, Fisher Weil theorem.
5. Spot and forward rate: forward rate implicit on spot rates.
6. Markowitz Theory: expected value, variance, stock portfolio, share expected return, share volatility, portfolio expected return, portfolio volatility, diversification effects, efficient portfolios, matrix notation, minimum variance portfolio, feasible set, efficient frontier, portfolio without shortselling.
7. Capital Asset Pricing Model: capital market line, tangent portfolio, market portfolio: basic comments.
8. Insurance, biomedical functions; life insurance: whole life insurance, term insurance. Pure endowments, endowment insurance. 
Examination methods:

The exam, using computer, will consist of 12 exercises with variable points (from 2 to 3, there aren’t penalties in the case of wrong answers) and their sum is 31 points. 
Assessment criteria:

The exam exercises have marks as follows:
1. Simple / compounding accumulation and discount (2 points),
2. Annuities (3 points),
3. Amortization schedule (3 points),
4. Internal Rate of Return, Net Present value, profit index (3 points),
5. Interest rate swap (3 points),
6. Bonds (3 points),
7. Spot and forward rates (2 points),
8. Financial Immunization (2 points),
9.Expected return, variance, minimum variance portfolio (3 points),
10. Capital asset pricing model (2 points),
11.Life insurance (3 points),
12 Net premiums (2 points). 
Course unit contents:

Simple and compound interest. Bonds, interest rate structure, portfolio theory, life insurance. 
Planned learning activities and teaching methods:

Lessons in front of the class: in these lessons the teacher will explain the theory and the exercises of the mathematics concerning the financial aspects listed above. In these lessons exercises included in the exam session will be discussed.
Every week, on the Moodle platform, exercises will be proposed to the students to practice their knowledge on the arguments developed during the lessons. These exercises, with automatic correction, will give to the student immediate information on her/his preparation level.
Some of these exercises will be proposed in flipped classroom modality, then the teacher or the students themselves will do them during the lessons, in this way the theory development will be facilitated using the technique of problem solving. 
Additional notes about suggested reading:

The .pdf and the .xls slides used during the lessons will be uploaded on the Moodle platform: students will be able to use them without restrictions.
Every lesson proposed using digital ink will be uploaded on the Moodle platform in the .pdf format.
If in the classroom the teacher can record the lessons (on mp3 format or video format), these recorded lessons will be uploaded on the Moodle platform or on another appropriate available support. 
Textbooks (and optional supplementary readings) 

Elisabetta Allevi, Gianni Bosi, Rossana Riccardi, Magalì Zuanon., Matematica Finanziaria e Attuariale. : Pearson, 2017.

David Lovelock, Marilou Mandel, A. Larry Wright, An Introduction to the Mathematics of Money. : Springer, 2007.

Innovative teaching methods: Teaching and learning strategies
 Flipped classroom
 Auto correcting quizzes or tests for periodic feedback or exams
 Active quizzes for Concept Verification Tests and class discussions
 Video shooting made by the teacher/the students
 Use of online videos
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 One Note (digital ink)
 Kaltura (desktop video shooting, file loading on MyMedia Unipd)
 Latex
 Excel
Sustainable Development Goals (SDGs)

