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 arbitrage
b) No-arbitrage pricing
c) Contingent claims
d) 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
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 one theoretical question. The use of calculators is allowed during the test. This is a closed-book test. Pass requires an 18/30 mark.
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Italian Fiscal Code
93009870234
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