# Unit MATHEMATICAL FINANCE

Course
Mathematics
Study-unit Code
55A00078
Curriculum
Matematica per l'economia e la finanza
Teacher
Alessandra Cretarola
Teachers
• Alessandra Cretarola
Hours
• 42 ore - Alessandra Cretarola
CFU
6
Course Regulation
Coorte 2022
Offered
2023/24
Learning activities
Affine/integrativa
Area
Attività formative affini o integrative
SECS-S/06
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
English.
Contents
Introduction to financial markets. Financial market models in discrete time. Financial market models in continuous time. Interest rate models.
Reference texts
1) D. Filipovic, Term-Structure Models: A Graduate Course, Springer Finance, Springer-Verlag, Berlin, 2009.

2) M. Musiela, M. Rutkowski, Martingale Methods in Financial Modeling, Springer-Verlag Berlin Heidelberg, 2005.

3) A. Pascucci, PDE and Martingale Methods in Option Pricing, Bocconi & Springer Series, 2011.

Further teaching material, such as updated notes from the lecturer, is available on Unistudium.
Educational objectives
Providing a solid introduction to the problems arising from modern Financial and to the mathematical methods to solve them. At the end of the course, the student theoretically knows the main topics related to mathematical modeling of financial markets and to pricing and hedging of the main derivatives under no arbitrage opportunities. In particular, the student is able to:

- use stochastic calculus instruments for a non-deterministic approach of financial markets;
- price the most important derivatives in markets under no arbitrage opportunities with the aware use of appropriate stochastic calculus methodologies;
- use the main models for the term structure of interest rates in pricing of interest rate derivatives.
Prerequisites
In order to be able to understand and apply the majority of the techniques described within the Course, you must know the fundamental concepts of Mathematical Analysis. In particular, the knowledge of standard differential and integral calculus in one or more variables is assumed. Moreover, having learned both the basic instruments of probability theory and the theory of Stochastic Processes, and bases of stochastic calculus is considered necessary.
Teaching methods
Face-to-face lectures on all the topics of the program.
Other information
1) Attendance: optional.

2) For students with Specific Learning Disorders and/or Disabilities please refer to the web page: http://www.unipg.it/disabilita-e-dsa
Learning verification modality
The examination includes an oral discussion. The oral exam consists in an interview of about 45 minutes long aiming to ascertain the knowledge level and the understanding capability acquired by the student on theoretical and methodological contents as indicated on the program. The oral exam will also test the student presentation skills and her/his autonomy in the organization and exposure of the theoretical topics.

The oral exam can be also taken in Italian, according to the student request.
Extended program
Introduction to financial markets: underlying assets and derivatives, types of traders in derivatives markets, problems of pricing and hedging of European-type contingent claims. Financial market models in discrete time: self-financing and predictable strategies, arbitrage and martingale measures, fundamental theorems of asset pricing, binomial model, trinomial model as an example of incomplete market.
Financial market models in continuous time: self-financing and predictable strategies, arbitrage and martingale measures, complete markets; diffusion models, Black & Scholes model, change of numéraire, valuation of European-type options.
Interest rate models: short-rate models, affine term structures, bond pricing, Heath–Jarrow–Morton methodology and forward rate models, forward measures.
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