SUBJECT

Econophysics

lecture

master

Faculty of Science

Physics MSc

3

Semester 3

Autumn semester

Extreme statistics, Fischer-Tippet theorem and applications in risk assessment;

Central limit theorem, stable distributions, attraction pools, centrality and norm constant choices, speed of convergence, large deviations;

Random matrices, Wigner surmise, Wishart matrices, Marchenko-Pastur theorem.

Multivariate distributions, copulae. Price fluctuations on real markets, empirical stylization, non-stationary behavior (ARCH-GARCH models). Portolio and risk measures: elliptical distributions, portfolio optimization, value-at-risk, variance as risk measure, absolute deviation, expected shortfall, maximal loss, coherent and spectral measures. Financial regulation examples (Basel I, II and III, order book regulations). Instability of portfolio optimization, divergence of estimation error, fluctuating weights, noise reduction (cleaning), simulated markets, Cholesky decomposition. Derivatives (forward, swap, options) and their pricing methods, Black-Scholes formula, interpretation of the smile curve, remaining risk.

recommended readings:

• J.-Ph. Bouchaud és M. Potters: Theory of Financial Risks, Cambridge University Press, 2000
• R.N. Mantegna és H.E. Stanley: An Introduction to Econophysics – Correlations and Complexity in Finance, Cambridge University Press, 2000