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37503 - Quantitative Finance

Academic Year 2021/2022

                
                        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)

                            Teaching resources on Virtuale

Course contents

No arbitrage pricing, single period discrete models
Probability space, sotchastic processes, 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.

Readings/Bibliography

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

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

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

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

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.

Office hours

See the website of Lorenzo Torricelli