Download Financial Mathematics

Code 27003011
Description Financial Mathematics
Sector Code SECS-S/06
Single Module Type OB
Weight 10
Course Year 2
Cycle type Code S2
Apprenticeship NO
Lingua di insegnamento Italian
Contenuti
1. Basic concepts of financial mathematics. Interest, interest rate, discount rate, instantaneous interest rate,
in spot and future basic financial operation. The simple interest function and the compound interest
function. The exponential interest function. Equivalent rates in simple and compound interest functions.
Nominal rates. Zero coupon bond and coupon bond. 2. The value of a financial operation. Present value and
future value. Fair financial operation respect to a financial function. Properties of the exponential interest
function. Net present value as choice criterion between financial operations. 3. Annuity and mortgage loan.
Annuity definitions. Present value and future value of temporary annuity (anticipated, posticipated,
immediate and deferred, temporary and perpetual). Mortgage loan definitions. Amortization schedule.
Mortgage loan with constant payment, Mortgage loan with constant principal, Mortgage loan with final
payment. 4. Internal Rate of Return. Definition of Internal Rate of Return (IRR) in a financial operation.
condition of existence and uniqueness of the IRR. Cartesium theorem. Cases with analytical solution for the
IRR. Numerical methods for the determination of the IRR: the secant method. The IRR as choice criterion
between financial operations. 5. Time and volatility index. Maturity, time to maturity, average maturity and
Macaulay duration. Portfolio Duration, Fixed bond duration. The Macaulay duration as volatility index.
Percentage variation of the cash flow value. 6. Value function and market prices. Market assumption:
frictionless, competitiveness and arbitrage free. Zero coupon bond. The linearity of the present value. Value
function in spot and forward contract. The term structure of interest rate. 7. Introduction to the
immunization theory. Interest rate risk. Classic immunization theory. The theorem of Fisher and Weil and
Redington’s theorem. 8. Elements of utility theory. The problems of the choice between stochastic financial
operation. Remarks on the axiomatic approach. Preference ordering on the opportunity set. First order
stochastic dominance. Theorem of von Neumann and Morgenstern. The expectation criterion. The Saint
Petersburg paradox. The expected utility criterion (certainty equivalent). Risk aversion, and risk propensity.
Utility function differential properties. Absolute measure of risk aversion. Some kinds of utility functions:
(logarithmic, exponential and quadratic). Quadratic approximation of the utility function. Mean-variance
criterion. Minimum variance portfolio (the two assets case). Insurance policies and utility theory:
elements.
Testi di riferimento Moriconi F., De Felice M., La teoria dell’immunizzazione finanziaria, Il
Mulino, 1991 Moriconi F., Matematica finanziaria, Il Mulino, 1995. Cacciafesta F., Matematica
Finanziaria (classica e moderna) per i corsi triennali, Giappichelli, 2006 Massabò I., Costabile M.,
Esercizi di Matematica Finanziaria
Obiettivi formativi the course aims at providing to the students the basic concept of the financial
mathematics and the preparation for the computation of the fundamental measures in deterministic
financial operation. It also aims at providing to the students le knowledge of the concepts needed
for the evaluation of simple non deterministic financial operation.
Prerequisiti
none
Metodi didattici
self-study, lectures and exercises
Altre informazioni
Modalita di verifica dell'apprendimento
written and oral examination
Programma esteso
ID Number
010758
Last Name
MENZIETTI
First Name
MASSIMILIANO
Role Code
PA
Activity Type
LEZ
Hours
60