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)
3) Girsanov Theorem
4) Feynman-Kac Theorem
5) Self-financing portfolios
6) No-arbitrage pricing
7) The Black-Scholes formula and its derivation.
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.
|T. Bjork||Arbitrage theory in continuous time (Edizione 3)||Oxford University Press||2009||978-0-199-57474-2|
|F. Menoncin||Mercati finanziari e gestione del rischio||Isedi||2006|
There is a written test. In case the teacher has doubts on how to evaluate the student, the student is called for also an oral examination, which is compulsory
The test consists of practical exercises and theoretical questions, and can cover the whole programme of the course. The use of calculators is allowed during the test, while using notes or books or similar material is forbidden.
The exam is passed only if a mark of at least 18/30 is obtained.