2022/2023

2022/2023

DM270

FIS/02 (THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS)

DEPARTMENT OF PHYSICS

Fisica teorica

1°

1st semester (26/09/2022 - 13/01/2023)

6

48 lesson hours

Italian

ORAL TEST

MONTAGNA GUIDO (titolare) - 6 ECTS

A good knowledge of the fundamental concepts of probability and statistics. Basic university preparation in mathematics and physics, with particular reference to ordinary and partial differential equations. A knowledge of the main results of Statistical Mechanics is welcome.

The course is an introduction to the role played by statistical physics, and particularly the theory of stochastic processes, in the modeling of the dynamics of financial markets and main financial instruments. The course provides a window on the modern interdisciplinary applications of theoretical physics and could stimulate the interest of the students for a future professional role in the financial industry.

The main applications of the methods of theoretical physics to the modeling of the dynamics of financial markets are discussed. The first part of the course is devoted to the theory of stochastic processes, while the second part describes the role of stochastic processes in econophysics and finance.
Brownian motion and interpretations of Einstein and Langevin. Random walk, diffusion processes and link with the central limit theorem. Markov processes, Wiener processes and their properties. Fokker-Planck equation. Stochastic differential equations and elements of Ito stochastic calculus. Ito and Ornstein-Uhlenbeck processes.
Introduction to financial markets and instruments. Geometric brownian motion and lognormal distribution of stock prices. Options and Black-Scholes model. Limits of the Black-Scholes model. Exotic options and binomial trees. Interest rates, bonds and Vasicek model.
Empirical analysis of high-frequency financial data. Levy distributions and non-Gaussian models. Introduction to stochastic volatility models. Power laws in nature and society.

Lectures aimed at providing an illustration of all the conceptual and mathematical aspects inherent to each topic. All the necessary financial notions will be given, thus making the course self-consistent.

W. Paul, J. Baschnagel, Stochastic processes from physics to finance, Springer.
C.W. Gardiner, Handbook of Stochastic Methods, Springer.

Oral exam. The student will be asked to have acquired the theory of stochastic processes (in particular, the main rules of stochastic calculus) and its application to the modeling of financial markets and instruments.