69827 - Financial Mathematics A.C.

Learning outcomes

By the end of the course, students know the basic mathematical concepts and methods of financial mathematics. In particular, they know the stochastic calculus tools and the models that describe the evolution of stock prices and interest rates, and that allow one to value financial derivatives. Students are capable of - understanding traditional models for asset pricing; - performing simulations and numerical investigations based on these models.

Course contents

Basics of financial mathematics and probability theory;L stochastic processes; Wiener processes and martingales; stochastic differential equations; scochastic models (discrete and continuous) for stock prices and interest rates; Ito's stochastic calculus; financial options and no-arbitrage pricing; European options (Black-Scholes model), Amerian and exotic options; numerical approximation of option prices, computational aspects; Monte Carlo simulation (pricing by discounted expectation), the finite difference method; brief overview of credit risk, the Merton's model; introduction to Matlab.

Readings/Bibliography

Luca Ballestra, Matematica Finanziaria, McGraw-Hill Create, 2019, ISBN: 9781307461459

For a better understanding of the theoritical models and methods, the following textbook is suggested too:

Menoncin Francesco, Mercati finanziari e gestione del rischio, ISEDI, 2006

Teaching methods

The first part of the course consists of both theoretical lessons and practical exercises made by the teacher on the blackboard. Then, the second part of the course is hold in the computer lab, where students perform numerical simulations that implement the asset pricing models and the mathematical methods learnt during the theoretical lessons.

Assessment methods

Students will develop, also with the aid of the Matlab software, a project on a case study assigned by the teacher. Then, an oral examination follows on the main theoretical concepts andl notions taughtin the classroom.

The final grade in the overall exam (Mathematics) will be the average of the grades taken in the single modules (mathematical Analysis and Financial Mathematics).

Teaching tools

The theoretical lessons will be mainly taught at the blackboard, even if few slides will be used too. The practical simulations will be done in the computer lab, and they will be based on the matlab software.

Office hours

See the website of Luca Vincenzo Ballestra