Basic statistics and calculus
The course aim is to present the simplest and basic mathematical theories for derivatives pricing.
Futures and options. Arbitrage pricing theory. Values of European derivatives by the binomial model. Wiener’s process. Brownian motion. Random integrals. Ito’s lemma. Black and Scholes model. Solution by series. Formulas of options. Delta hedging. Greek parameters.
Estimation and elimination of trend and seasonal components in time series. Stationary process. Properties of sample mean and autocorrelation function. Innovations and Durbin-Levinson algorithm. ARMA models. Modelling and forecasting with ARMA models. ARIMA models. ARCH and GARCH process.
Paul Wilmott - Introduzione alla finanza quantitative - Egea
John C. Hull, Opzioni, futures ed altri derivati.
Peter J.Brockwell, Richard A.Davis – Introduction to time series and forecasting -
Lessons and software in order to solve exsercises and examples from the theory
Test during the course