EDUCATIONAL OBJECTIVES:
The primary training objectives are related to learning the main mathematical methods used in the evaluation of basic financial operations, in the study of the dynamics of interest rates and in investment and/or financing choices.
KNOWLEDGE AND UNDERSTANDING:
Students must demonstrate that they acquire knowledge of the different analysis methods both from the theoretical point of view and from the point of view of their practical applications in the financial field.
ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING:
At the end of their course, students are able to apply the knowledge acquired, determine the fair value of a financial transaction, apply objective and analytical criteria in financial decisions, as well as know how to evaluate the value of investments/financing.
INDEPENDENT JUDGMENTS:
The student must have made the concepts presented their own and be able to apply them critically and appropriately in financial decisions, whether internal to a company or relating to the financial markets.
COMMUNICATION SKILLS:
The student must be able to communicate the concepts learned effectively and with technical language skills.
LEARNING ABILITY:
The student must have developed adequate skills to be able to independently undertake the study of more advanced topics.

PROPEDEUTICS:
Student must know the topics covered in the course of Matematica generale.

PREREQUISITES:
In order to understand the topics dealt with in the course, basic concepts of mathematics are essential.

1. Financial operations
1.1 Introduction to financial operations
1.2 Types of financial operations
1.3 The principle of financial equivalence and the value function
1.3.1 Financial equivalence, capitalization and discounting
1.3.2 Value function, capitalization and discounting factor
1.3.3 Periodic interest rates and discount rates
1.3.4 The financial laws of intertemporal equivalence

2 The financial regimes
2.1 The simple interest financial regime
2.2 The advanced interest financial regime
2.3 The compound interest financial regime
2.4 Comparison between financial regimes
2.5 Capitalization by mixing regimes
2.6 Equivalent effective rates
2.6.1 Equivalent rates in the RIS
2.6.2 Equivalent rates in the RIA
2.6.3 Equivalent rates in the RIC
2.7 Nominal rates
2.8 Force of interest and force of discount
2.8.1 The general case
2.8.2 The general case with two-variable financial laws
2.9 Capitalization in continuous time
2.10 Financial divisibility

3 Annuities
3.1 Annuities and capital value
3.2 Capital value ​​for the different types of annuity
3.2.1 Full, immediate, temporary, in arrears annuity
3.2.2 Full, immediate, temporary, advance annuity
3.2.3 Full, deferred, temporary annuity
3.2.4 Full perpetual annuity
3.2.5 Fractional annuity
3.2.6 Annuities in continuous time
3.2.7 Annuity with varying installments
3.3 Problems related to annuities
3.3.1 Determine the annuity installments
3.3.2 Determine the annuity duration
3.3.3 Determine the return rate of an annuity
3.4 Applications of annuities
3.4.1 Capital accumulation
3.4.2 Repayment of a capital

4 Amortization
4.1 Fundamental quantities and relationships of depreciation
4.2 Types of amortization
4.2.1 Single repayment of principal and interest
4.2.2 Single repayment of capital and periodic interest
4.2.3 Gradual reimbursement
4.2.4 Pre-amortization
4.3 Uniform or Italian amortization
4.4 Progressive amortization with constant installments
4.5 Amortization with accumulation or American amortization
4.6 Progressive amortization with advanced interest or German amortization
4.7 Evaluation of a loan

5 Choice between financial operations
5.1 The Net Present Value criterion
5.2 The IRR criterion

6 The term structure of interest rates
6.1 The theory of financial equivalence and the financial market
6.2 Bonds and the bond market
6.2.1 Zero Coupon Bond and Coupon Bond
6.2.2 Clean price and dirty price
6.3 Financial operations in the market: spot and forward trading
6.3.1 The principle of no arbitrage
6.3.2 ZCB, spot prices and forward prices
6.3.3 ZCB portfolios: the linearity of the price of complex securities
6.3.4 From ZCB prices to interest rates
6.3.5 Yield to maturity in continuous time
6.4 The term structure
6.4.1 The term structure of prices
6.4.2 The term structure of interest rates
6.5 The measurement of the term structure: main methods

7 Temporal and variability indices: Macaulay duration, modified duration and convexity

De Angelis Paolo, De Marchis Roberto, Marino Mario, Martire Antonio Luciano, "Lezioni di matematica finanziaria", Giappichelli Editore, Terza Edizione, 2024.

Pianca Paolo, Basso Antonella, "Introduzione alla matematica finanziaria", CEDAM, Terza Edizione, 2017.

1. Financial operations
1.1 Introduction to financial operations
1.2 Types of financial operations
1.3 The principle of financial equivalence and the value function
1.3.1 Financial equivalence, capitalization and discounting
1.3.2 Value function, capitalization and discounting factor
1.3.3 Periodic interest rates and discount rates
1.3.4 The financial laws of intertemporal equivalence

2 The financial regimes
2.1 The simple interest financial regime
2.2 The advanced interest financial regime
2.3 The compound interest financial regime
2.4 Comparison between financial regimes
2.5 Capitalization by mixing regimes
2.6 Equivalent effective rates
2.6.1 Equivalent rates in the RIS
2.6.2 Equivalent rates in the RIA
2.6.3 Equivalent rates in the RIC
2.7 Nominal rates
2.8 Force of interest and force of discount
2.8.1 The general case
2.8.2 The general case with two-variable financial laws
2.9 Capitalization in continuous time
2.10 Financial divisibility

3 Annuities
3.1 Annuities and capital value
3.2 Capital value ​​for the different types of annuity
3.2.1 Full, immediate, temporary, in arrears annuity
3.2.2 Full, immediate, temporary, advance annuity
3.2.3 Full, deferred, temporary annuity
3.2.4 Full perpetual annuity
3.2.5 Fractional annuity
3.2.6 Annuities in continuous time
3.2.7 Annuity with varying installments
3.3 Problems related to annuities
3.3.1 Determine the annuity installments
3.3.2 Determine the annuity duration
3.3.3 Determine the return rate of an annuity
3.4 Applications of annuities
3.4.1 Capital accumulation
3.4.2 Repayment of a capital

4 Amortization
4.1 Fundamental quantities and relationships of depreciation
4.2 Types of amortization
4.2.1 Single repayment of principal and interest
4.2.2 Single repayment of capital and periodic interest
4.2.3 Gradual reimbursement
4.2.4 Pre-amortization
4.3 Uniform or Italian amortization
4.4 Progressive amortization with constant installments
4.5 Amortization with accumulation or American amortization
4.6 Progressive amortization with advanced interest or German amortization
4.7 Evaluation of a loan

5 Choice between financial operations
5.1 The Net Present Value criterion
5.2 The IRR criterion

6 The term structure of interest rates
6.1 The theory of financial equivalence and the financial market
6.2 Bonds and the bond market
6.2.1 Zero Coupon Bond and Coupon Bond
6.2.2 Clean price and dirty price
6.3 Financial operations in the market: spot and forward trading
6.3.1 The principle of no arbitrage
6.3.2 ZCB, spot prices and forward prices
6.3.3 ZCB portfolios: the linearity of the price of complex securities
6.3.4 From ZCB prices to interest rates
6.3.5 Yield to maturity in continuous time
6.4 The term structure
6.4.1 The term structure of prices
6.4.2 The term structure of interest rates
6.5 The measurement of the term structure: main methods

7 Temporal and variability indices: Macaulay duration, modified duration and convexity

Lectures

Teaching material is available on the Teams platform dedicated to the course.

Non-attending students are invited to contact the teacher for further suggestions on the course program and bibliographic references.

Written test consisting of two theoretical open-ended questions and three numerical questions to be solved and commented.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)