Learning objectives
In the first part of the Course basic quantitative tools are introduced in order to approach quantitative finance. In particular functions in several variables and probability are presented.
Modern finance is today an extremely rich field and often uses complex mathematical tools. The purpose of second part of the course is to present the main topics of quantitative finance in a clear and accessible way with the aim to stimulate intuition without abandoning the aspects of formalization that are now indispensable for anyone wishing to operate on financial markets.
Course unit content
Functions in several variables.
Maximum and minimum points with and without constraints.
Probability. Sample space, algebras and sigma-algebras.The axioms.
Random numbers. Expected value. Variance and covariance.
Markets.
Shares, goods, currencies, forward, futures contracts and options.
Options: the binomial model.
The binomial tree. The value of an option. Arbitrage and non-arbitrage.
The drift. Volatility. The Wiener process. Basic knowledge of stochastic calculus. Ito's lemma. Random walks.
The Black and Scholes model.
Towards elimination of risk: hedging.
Bibliography
E. Castagnoli, M. Cigola, L. Peccati, La matematica in azienda 2: complementi di analisi, Milan, Egea, 2010.
E. Castagnoli, M. Cigola, L. Peccati, Probability, Milan, Egea, 2009.
John C. Hull, Opzioni, futures e altri derivati, Milan, Pearson - Prentice Hall, 2009.
