Mathematical finance (2018/2019)

Course code
4S001142
Name of lecturer
Luca Taschini
Coordinator
Luca Taschini
Number of ECTS credits allocated
9
Academic sector
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
Italian
Period
secondo semestre lauree magistrali dal Feb 25, 2019 al May 31, 2019.

Lesson timetable

Go to lesson schedule

Learning outcomes

The course offers an introduction to arbitrage theory and its applications to financial derivatives pricing in discrete and continuous time.

Syllabus

First part: No arbitrage principle in discrete time

1) Binomial model (one-period and multi-period)
a) Portfolio and no-arbitrage pricing
b) Contingent claims
c) Risk neutral valuation
2) The absence of arbitrage
3) First and Second Fundamental Theorems
4) Martingale pricing
5) Market completeness

Second part: No-arbitrage principle in continuous time

1) Stochastic calculus: stochastic differential equations (basics)
2) Martingales
3) Girsanov Theorem
4) Feynman-Kac Theorem
5) Self-financing portfolios
6) No-arbitrage pricing
7) The Black-Scholes formula and its derivation.
8) Delta-hedging

Textbooks and references
1) Bjork, T., Arbitrage theory in continuous time, 2nd Edition, Oxford University Press, 2004.
2) F. Menoncin: Mercati finanziari e gestione del rischio. Isedi, 2006.

Reference books
Author Title Publisher Year ISBN Note
T. Bjork Arbitrage theory in continuous time (Edizione 3) Oxford University Press 2009 978-0-199-57474-2
Desmond J. Higham e Nicholas J. Higham MATLAB Guide SIAM 2005
F. Menoncin Mercati finanziari e gestione del rischio Isedi 2006

Assessment methods and criteria

There is a written test.

The test consists of exercises and a theoretical question. The use of calculators is allowed during the test.

Pass requires an 18/30 mark.

Student opinions - 2017/2018