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’.
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.
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.
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.
Learning skills: The course features typical aspects of applied mathematics. A modicum degree of mathematical sophistication is required. Students are provided with exercises, whose solutions are discussed during the classroom. Students are strongly required to ask questions concerning theoretical and practical aspects of the treated financial models and techniques.
The financial calculus needed will be developed through Lectures to be held during the classroom, Sometimes, real world cases consist of numerical evaluation using Excel spreadsheets developed during the classroom. Furthermore, students are asked to solve exercises to test their understainding of the main financial definition, theorems and formulas.
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.
S. A. Broverman, Mathematics of Investments & Credits, Egea, 2019