FINANCIAL MATHEMATICS

Course objectives

The primary learning outcome of this subject is to allow students to learn theoretical elements and basic mathematical instruments to evaluate elementary financial operations. Furthermore, students must know how to interpret the results of their application to real problems. Specific objectives Knowledge and understanding: After attending the course, students know and understand the problems related to the evaluation of the basic financial operations and mathematical models to be used to solve such problems. Capacity to apply knowledge and understanding: At the end of the course, students can formalize basic financial operations, according to the correct mathematical approach and apply specific models of the subject, to solve evaluation problems. Autonomous judgment: At the end of the course, students can collect and read data concerning basic and complex financial, borrowing-and-lending as well as investment operations, also in a context governed by fixed or varying interest rates. Communication skills: At the end of the course, students can explain and represent problems and solutions in the financial field, through the methods acquired. Learning skills: At the end of the course, students acquired basic financial logic that will allow them to approach further studies in the area of theories and processes of complex financial markets.

Channel 1
SERGIO BIANCHI Lecturers' profile
Channel 2
MASSIMILIANO FREZZA Lecturers' profile

Program - Frequency - Exams

Course program
Definition and classification of financial operations. Basic financial operations. Principle of financial equivalence. Assumptions of the ideal market. Characteristics of real financial markets. Schemes of investment and anticipation financial operations. Assumptions regarding price functions. Capitalization factor. Discounting factor. Interest. Effective interest rate. Discount. Effective discount rate. Spot and forward financial operations. Properties of value functions in the context of forward schemes. Relationship between spot and forward operations (in the case of two periods). No-arbitrage condition. Market structure based on interest rates. Financial regimes. Financial regime of compound capitalization (periodic rate, variable rates, average rate). Equivalent rates. Nominal interest rate convertible. Instantaneous interest intensity. Nominal discount rate convertible. Instantaneous discount intensity. Interest force for financial laws of one variable. Interest force for financial laws of two variables. Divisibility. Uniformity. Financial regime of simple capitalization. Financial regime of commercial discounting. Complex financial operations. Annuities. Valuation of an annuity. Internal rate of return. Classification of annuities. Present values and amounts for immediate, deferred, advanced, postponed, whole, and fractional annuities. Present values for perpetuities. Present values and amounts for continuous annuities. Mixed capitalization (overview). Determining the number of installments, the installment amount, and the interest rate. Rate search problem: iterative method, interpolation method, and successive approximation method. Temporal and variability indices. Maturity. Financial average maturity. Arithmetic average maturity. Duration: definition, properties, and financial interpretation. Duration of fixed-coupon securities. Convexity: definition and classification. Bond loans. Duration of: bonds (TCN, TCF), bond portfolios (with examples), immediate deferred annuity with constant installments and properties. Convexity. Capital formation and amortizations. Issues related to capital formation. Loan contract (generalities). Residual debt. Settled debt. Capital portion. Interest portion. Installment. Amortization: classification. Amortization with periodic interest payments and final capital repayment. Progressive amortization. Uniform amortization. Amortization with two rates. Amortization with prepaid interest.
Prerequisites
Calculus
Channel 3
Lecturers' profile
Lecturers' profile
  • Lesson code1017164
  • Academic year2025/2026
  • CourseBusiness sciences
  • CurriculumGestione d'impresa
  • Year2nd year
  • Semester2nd semester
  • SSDSECS-S/06
  • CFU9
  • Subject areaStatistico-matematico