Basic Concept of Econophysics

Introduction to Econophysics; definitions of main terms of finances. Markets as complex systems; chaos, fractals and multifractals (brief overview). Probability distributions: Gaussian statistics, Poisson distribution, Lévy distribution, fat tails, Pareto-Zipf’s law. Simple models of markets (efficient Market hypothesis, random walks, scaling in financial data). Stochastic processes and stochastically forced dynamical systems. Time series analysis for financial data: fractal and multifractal analysis, wavelet transform method. Single financial time series: stylized facts. Multiple financial time series: linear and nonlinear cross-correlations; factor analysis. Options and the Black-Scholes model (time dependent model for equity valuations used in option pricing). Risk management; portfolio variance minimization. Portfolio optimizations: time horizons, market predictions, market impact, and target functions.

NB! This course will take place in autumn semester 2025/2026 which starts on 1st of September and ends on 25th of January (you can find that information under Start date section). TalTech's timetables for Autumn semester 2025 will be published at the end of June via tunniplaan.taltech.ee. Switch the page to English and use "Search" and "Open detailed search" to find your course. NB! Some courses are taught by several lecturers during the same semester. Make sure that the course name and lecturer/teacher infromation of your course match with the information given in the Course Catalogue.

Knows fundamental concepts and methods of econophysics: Gaussian and non-Gaussian fluctuations, power law distributions, self-affine and multifractal time series, Black-Scholes model, cross-correlations of multivariate time series and factor analysis, efficient Market hypothesis, target functions and portfolio optimization, scale-free networks.

Final assessment can consist of one test/assignment or several smaller assignments completed during the whole course. After declaring a course the student can re-sit the exam/assessment once. Assessment can be graded or non-graded. For specific information about the assessment process please get in touch with the contact person of this course. For specific information about grade transfer please contact your home university

None.

• Main textbook. Rosario N. Mantegna and H. Eugene Stanley, An Introduction to Econophysics, Correlations and Complexity in Finance, Cambridge University Press, Cambridge, UK
• Supplementary textbook: Econophysics: An Introduction Sitabhra Sinha, Arnab Chatterjee, Anirban Chakraborti, Bikas K. Chakrabarti
• ISBN: 978-3-527-40815-3

lectures, exercises