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

Lectures (blackboard, slide presentations) during which the main definitions of financial quantities relevant to the course will be presented. In certain cases, theorems will be presented and discussed, requiring a minimum level of mathematical sophistication from the student. Where necessary, some of the prerequisites of general mathematics will be revisited in class. A selection of exercises with solutions will be presented during the lecture. Some topics will be illustrated using Excel spreadsheets when appropriate.

Required Prerequisites

While there are no formal prerequisites, knowledge of the following mathematics topics is considered "essential." The four operations and their properties; prime numbers, prime factorization, greatest common divisor, and least common multiple; fractions and operations with fractions; powers, roots, and logarithms; monomials, polynomials, and polynomial factorization; first and second-degree equations; lines, line segments, angles, triangles, perpendicular and parallel lines. Pythagoras' theorem. Arithmetic and geometric progressions (finite and infinite). It is also useful to have knowledge of the General Mathematics curriculum of the same degree program.

Attendance of Lessons

Highly recommended

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

S. A. Broverman, Mathematics of Investments & Credits, Egea, 2019

Learning Assessment

Learning Assessment Procedures

The exam aims to assess the achievement of the educational objectives and consists of a mandatory written test with open-ended questions. Booking for the written test is compulsory. The written test aims to verify the student's ability to use and apply basic concepts, tools, and fundamental results proposed in the program, using the appropriate mathematical language. The grade will be assigned based on the level of preparation demonstrated by the student, while passing the exam requires reaching a minimum threshold of knowledge in the topics covered in the course program. The maximum score for the written test is 30 points, and the test is considered passed if a score of at least 18 is obtained.