FINANCIAL MATHEMATICS A - L

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 by product, this help 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 progession 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 sigle repayment of the principal (general and periodic); several interest repayments and sigle 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 evaluatimg 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. Comparision 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: parrallel and nonparallel shifts. Time indexes: arithmetic mean maturity; duration and modified duration. Convexity.

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 (suggested textbook)
3. P. Zima, R. L. Brown, Matematica Finanziaria, McGraw-Hill, Shaum’s, 1997
4. F. Moriconi, Matematica finanziaria, Il Mulino, Bologna