37503 - Quantitative Finance

Academic Year 2019/2020

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Economics and Economic Policy (cod. 8420)

Learning outcomes

The aim of the course is to provide students with the main probabilistic tools needed to approach modern finance based on the arbitrage theory.

Course contents

Basics on probability calculus. Sequences of random variables. Stochastic processes. Martingales. Central limit theorem. Brownian motion. Ito's lemma. Exponential martingales. Changes of measure in the discrete case. Girsanov's theorem. Basic facts about heat equation.

Applications to finance: Arbitrage-free markets. Self-financing portfolio. Complete markets: the binomial model and the Black and Scholes model. European options. Pricing and hedging techniques.

Readings/Bibliography

Teacher's Lecture Notes downloadable from the University web site.

Bibliography:

Baxter-Rennie, Financial calculus- An introduction to derivative pricing, Cambridge University press 1997

De Giuli- Maggi-Magnani-Rossi, Derivati- teoria ed applicazioni, Giappichelli, 2002

Lamberton, Lapeyre, Introduction to stochastic calculus, Chapman and Hall, 1996

Pascucci,Calcolo stocastico per la finanza, Springer

Teaching methods

Classes

Assessment methods

Written exam with four theoretical questions and four exercises.

Teaching tools

Blackboard

Office hours

See the website of Sabrina Mulinacci