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