Introduction to probability and mathematical statistics with a special focus on economic and financial applications.
Contenuto del corso
Valore attuale, interesse semplice e composto, inflazione. Tasso Interno di Rendimento. Rendite, ammortamenti e mutui. Obbligazioni, duration e convexity. Pricing di opzioni call/put. Introduzione a Excel.
D.Lovelock, M.Mendel, A.L. Wright – An Introduction to the Mathematics of Money, Springer
Obiettivi Formativi
The students will be able to solve simple problems where the random model is required for economic and financial applications. They will be able to formalize the problem, solve it and present their results.
Obiettivi Formativi
Capire l'importanza di concetti di base quali: valore del denaro nel tempo, composizione degli interessi, obbligazioni e opzioni. Essere in grado di risolvere semplici problemi finanziari, anche tramite l'uso di Excel.
Prerequisiti
Basic Calculus
Prerequisiti
Basi del Calcolo (limiti, derivate, funzioni log e exp)
Metodi Didattici
Classroom lectures and homeworks
Metodi Didattici
Lezioni in presenza, con sessioni di esercizi e di esempi in Excel.
Altre Informazioni
A positive grade (greater or equal 27/30) in this workshop will be valued as sufficient to meet the requirements of the preliminary test in Probability for the course in Quantitative Finance and Derivatives (MSc Finance and Risk Management)
Modalità di verifica apprendimento
Attending students:
Intermediate Tests and Final Presentation
Non Attending students: Final written exam with exercises on the whole program
Modalità di verifica apprendimento
Esame scritto
Programma del corso
Combinatorics, probability and conditional probability, independency, Bayes formula will be introduced motivated by the applications in economics and financial markets. Lotteries and probabilistic paradoxes.
Discrete random variables, and their distributions: Bernoulli, Binomial, Geometric, Poisson distributions.
Applications to statistical inference, VaR, financial default.
Random models: random walk and Markov chain. Applications: asset price models, option pricing, credit rating.
Continuous random variables. Basic elements of integration theory. Uniform, Exponential, Normal distributions.
Expectation, variance, skewness, curtosis.
Gaussian approximation. Application to finance and risk management.
Programma del corso
- Interesse semplice e composto
- Tasso Interno di Rendimento
- Rendite e ammortamenti
- Obbligazioni
- Opzioni call/put
- Introduzione a Excel