- Docente: Lorenzo Torricelli
- Credits: 5
- SSD: SECS-S/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Economics and Economic Policy (cod. 8420)
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from Nov 07, 2023 to Dec 12, 2023
Learning outcomes
Thoe course aims at intoducing the basic concepts for the quantitative analysis of financial problems. At the end of the course students should to show understanding of the main mathematical tools for the dynamic modelling of financial markets, such as discrete and continuous-time stochastic processes, They should be able to apply the theory of no-arbitrage pricing for financial products, determine hedging strategies, apply models to real data interpreting the results.
Course contents
- No arbitrage pricing, single and multi eriod discrete models
- Probability spaces, stochastic processes, Brownian motion, stochastic calculus, Martingales, maritngale representation theorem
- Risk-Neutral measure. Fundamental theorem of asset pricing. Measure changes, Girsanov Theorem. Stochastic discount factors. Numeraire.
- Self-financinge portfolios, hedging, completeness. PArabolic equations and financial valuation, Feynman-Kac theorem.
- Samuelson-Black-Scholes model, options, greeks. Implied volatility.
- 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
Whiteboard, tablet
Office hours
See the website of Lorenzo Torricelli