78355 - QUANTITATIVE FINANCE

Conoscenze e abilità da conseguire

The aim of the course is to give students the specific expertise for the quantitative analysis of financial problems. At the end of the course we expect students to: - have mastery of the main mathematical tools (continuous and discrete time stochastic processes) necessary for the dynamic modelling of the markets; - be able to price financial products coherently with the no arbitrage principle; - know how to determine the optimal investment strategy; - be able to apply the investigated theoretical models to real data and interpret the results.

Contenuti

1. No arbitrage pricing, single and multiperiod discrete models
   
2. Probability spaces, stochastic processes, Brownian motion, stochastic calculus, Martingales, martingale representation theorem
3. Risk-Neutral measure. Fundamental theorem of asset pricing. Measure changes, Girsanov Theorem. Stochastic discount factors. Numeraire.
   
4. Self-financinge portfolios, hedging, completeness. PArabolic equations and financial valuation, Feynman-Kac theorem.
5. Samuelson-Black-Scholes model, options, greeks. Implied volatility.
6. Basics on Fixed income and products depending on more than one underlying

Testi/Bibliografia

M. Baxter, A. Rennie, Financial Calculus, Cambridge University Press, 1996

R. Elliott, P.E. Kopp, Mathematics of Financial Markets, Springer 2004.

S.E. Shreve, Stochastic Calculus for Finance I & II, Springer, 2013.

T. Björk, Arbitrage Theory in Continuous Time, Oxford University Press, 2004

E. Rosazza-Gianin C. Sgarra, Esercizi di Finanza Matematica, Springer, 2007.

Metodi didattici

Lectures

Modalità di verifica e valutazione dell'apprendimento

Written exam. Both exercises and theoretical questions will be presented. Supplementary interviews are possible.

Strumenti a supporto della didattica

Blackboard, Tablet

 

Orario di ricevimento

Consulta il sito web di Lorenzo Torricelli