# MATEMATICA PER L'ECONOMIA, L'IMPRESA E LA FINANZAModule MATEMATICA PER LA FINANZA

**Academic Year 2023/2024**- Teacher:

**MARIA ROSARIA PAPPALARDO**

## Expected Learning Outcomes

**1) Knowledge and understanding**:
The course addresses concepts of basic financial calculus under
certainty. Financial ideas and language are developed for a smooth
transition from basic techniques (e.g. simple and coumpound interest,
present value, etc.) to the concepts of fixed incme securities
evaluation, duration and immunization. The course emphasizes financial
real world applications together with the critical understanding of the
financial ‘jargon’.

**2) Applying knowledge and understanding**:
The techniques of financial calculus gradually learned should be
applied to model concrete problems, and then to solve them, acting as a
practitioner working in a context where a financial evaluation is needed (e.g. to
create an ammortization schedule). To this end, real world cases are
discussed and critically analyzed during the classroom.

**3) Making judgments**: The
interaction between students and the instructor aims to stimulate their
ability to judge the treated financial models and techniques. Students
should be able to revise them by the aid of information sources such as
journal articles, dataset, etc., also available on the web.

**4) Communication skills**: The
learning process (with a modular structure) is intended to provide
students with proper language and notation from the financial calculus.
Students are expected to critically understanding and to circulate them
as they acted in a real financial context.

**5) Learning skills**: The
course features typical aspects of applied mathematics. A modicum degree
of mathematical sophistication is required. Students
are strongly required to ask questions concerning theoretical and
practical aspects of the treated financial models and techniques.

## Course Structure

## Required Prerequisites

## Attendance of Lessons

## Detailed Course Content

**PART 1 (3 CFU)**

*Financial conventions, annuities, amortizations, founding capital*

**Learning goals:** Providing
both the theory and practice of elementary financial calculus under
certainty. As a by-product, this helps to develop professional skills.

**Topic description:** The
financial function and its properties. Financial convention: simple,
commercial, and compound; mixed cases; rational vs. commercial discount.
Equivalent interest rates, nominal interest rates, instantaneous
convention. Annuities and their classification: general discrete,
periodic, constant, fractional, continuous, perpetual. Annuities in
the compound convention: periodic arithmetic and geometric progression
payment; perpetuities. Inverse problems. Unshared loan and amortization:
general properties. Compound convention in amortization: Single
settlement repayment; multiple settlement repayments: general weak
amortization installments; several interest repayments and single
repayment of the principal (general and periodic); several interest
repayments and single repayment of the principal with collateral funding
of the principal: general case. American amortization. Italian
amortization. French amortization. German amortization. Cession’s value
of rights concerning a loan’s amortization. Capital accumulation:
discrete case.

**PART 2 (3 CFU)**

*Valuation of financial and real investments*

**Learning goals:** Providing
the theory and the main techniques for evaluating both financial and
real investments. Explaining the concept of interest rate risk and the
corresponding techniques of immunization.

**Topic description:** Loan
evaluation and general investment evaluation. Bare ownership and
usufruct. Investments in real markets under certainty. Some useful
criteria of investment evaluation: Net

Present Value (NPV); Internal Rate of Return (IRR); Payback period. Comparison among criteria. Shared loan amortization: basic concepts.
Constant amortization installments, constant reimbursement price. The effective rate for the issuer; the cession’s value of the credit; and the effective
rate for the holder. Cession’s value of a bond. Bond’s market: prices vs.
rates/yields. Zero coupon bonds. Fixed coupon bonds. The structure of
the market. Forward rates and spot rates. Immunization: basic
principles. Interest rate risk. Theorems of immunization: parallel and
nonparallel shifts. Time indexes: arithmetic mean maturity; duration and
modified duration. Convexity.

## Textbook Information

*Mathematics of Investments & Credits*, Egea, 2019

## Learning Assessment

### Learning Assessment Procedures

**VERSIONE IN ITALIANO**