Master’s degree in Banking and Finance

Mathematical finance

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

Site

VERONA

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.

Assessment methods and criteria