78355 - QUANTITATIVE FINANCE

Learning outcomes

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.

Course contents

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

Readings/Bibliography

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.

Teaching methods

Lectures

Assessment methods

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

Teaching tools

Blackboard, Tablet

Office hours

See the website of Lorenzo Torricelli