# FINANCIAL MATHEMATICS A - L

SECS-S/06 - 6 CFU - 2° Semester

SALVATORE GRECO

## Detailed Course Content

MODULE # 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 byproduct, 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 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.
MODULE # 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. Effective rate for the issuer; cession’s value of the credit; 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

1. F. Cacciafesta, Lezioni di matematica finanziaria classica e moderna, Giappichelli,Torino, 2001

2. R. L. D’Ecclesia, L. Gardini, Appunti di Matematica Finanziaria I, VII edizione, Giappichelli, Torino, 2013

3. F. Moriconi, Matematica finanziaria, Il Mulino, Bologna, 1994

4. B. Matarazzo, Sulla scelta degli investimenti privati, Catania

5. E. Volpe di Prignano, Lezioni di matematica finanziaria avanzata, CISU, 2009

Open in PDF format Versione in italiano