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.
Course Prerequisites
A good knowledge of the fundamental concepts of probability and statistics. Basic university preparation in mathematics and physics, with particular reference to the solution of ordinary and partial differential equations. A knowledge of the main results of Statistical Mechanics is welcome.
Teaching Methods
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.
Assessment Methods
Oral exam. The student will have to show to be familiar with the theory of stochastic processes (in particular, the main rules of stochastic calculus) and its application to the modeling of financial markets and instruments.
Face-to-face examination. Exceptions for fragile students.
Texts
C.W. Gardiner, Stochastic Methods - A Handbook for the Natural and Social Sciences, Springer.
W. Paul and J. Baschnagel, Stochastic processes from physics to finance, Springer.
R. N. Mantegna and H. E. Stanley, An introduction to econophysics: correlations and complexity in finance, Cambridge University Press.
Contents
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. Path integral. 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. Black-Scholes formulae and their interpretation. Limits of the Black-Scholes model and implied volatility. 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.
