Code

COMPG001

Year

MSc

Prerequisites

Term

2

Taught By

Tomaso Aste (100%)

Aims

The course is aimed at introducing to the statistical study of financial market data. The course is primarily focused on the observation of financial market dynamics of both individual assets and collective group of assets and the individuation of regularities, patterns and laws from a statistical perspective. Instruments to characterize, parameterize and model complex financial datasets will be introduced. Practical issues on data analysis and statistics of high frequency and low frequency financial data will be covered.

Learning Outcomes

Students will become able to analyze main statistical features of complex financial datasets. On successful completion of the course, a student should have a good understanding on: 1) the empirical probability distributions of financial returns; 2) how to characterize and parameterize these distributions; 3) the structure of inter-dependency between financial fluctuations in markets and its quantification; 4) some of the essential features of the complex dynamics of financial markets.

Applications:

There is a great need to increase the capability of observing and characterize real financial data. Instruments and tools provided by this course are essential to properly estimate risk from a sound scientific perspective.

Empirical investigation of financial markets

Essential practical familiarization with financial data concerning: equities, FX, interest-rates, commodities, low frequency and high frequency data sets, order book data. Stylized facts.

Fluctuations of a single variable

Statistical distribution of returns. Risk and large fluctuations. Moments of the distribution, excess kurtosis. Non-Gaussian distributions. Stochastic processes with non-defined variance. Stable distributions. Infinitely divisible distributions. Generalized extreme value distribution. Estimation methods to characterize the tails of the distributions.  Gaussian vs. non-Gaussian modeling. Calibration issues.

Collective fluctuations

Joint probability, marginal probability and conditional probability. Multivariate distributions: Gaussian, Student, Stable. Dependency between variables. Measure of dependency: linear correlation, rank correlation, Kendall’s tau correlation and correlation ratio. Mutual information. Transfer entropy. Decoupling marginals and dependency. Real-world dependency: common influence, cause and effect, spurious correlations. Correlation filtering though networks. Calibration and Application issues.

Complex dynamics

Non-Brownian motion. Fractal and multi-fractal nature of signals. Scaling laws. Persistence, anti-persistence and autocorrelation.

3 hours of lectures per week

The course has the following assessment components:

Written Examination (2 hours, 100%)

To pass this course, students must: 
 Obtain an overall pass mark of 50% for all sections combined

Y. G. Sinai, Probability Theory: An Introductory Course, Springer-Verlag, 1992.

Statistical Inference, G Casella and RL Berger, Thomson Learning 2002.

Further books and other resources will be indicated during the course.