• About SNS

    The Scuola Normale Superiore is a public institute for higher education that in its two centuries of life has earned itself a special place, both in Italy and abroad, a place characterised by merit, talent and scientific rigour.  Two types of course are available: the undergraduate course and the PhD course.The teaching activity is distributed among three academic structures: the Faculty of Humanities, the Faculty of Mathematical and Natural Sciences, placed in Pisa, and the Institute of Humanities and Social Sciences, located in Palazzo Strozzi in Florence. 

  • Admission

    The evaluation for entrance to the first year of the undergraduate course does not include the high school leaving certificate, and the bachelor's degree is not taken into consideration in the entrance examination for the fourth year course. For each PhD course, candidates’ level of competence, talent, motivations and aptitudes to scientific research will be assessed on the basis of their qualifications and research project and an interview.

  • Academics

    The Scuola Normale Superiore offers two types of course: the undergraduate course, leading to first and second level university degrees, and the PhD course, the international equivalent of the Italian Dottorato di ricerca.The teaching and research activity is distributed among three academic structures: the Faculty of Humanities, the Faculty of Mathematical and Natural Sciences, and the Institute of Humanities and Social Sciences.The first two academic structures, housed at the Pisa site, organize courses for both the  undergraduate course and the PhD course. The Institute of Humanities and Social Sciences, situated in Palazzo Strozzi in Florence, deals only with the PhD course.

  • Research

    A highly qualifying feature of the Normale way is the strong link between teaching and research that is a characteristic of both the undergraduate and the graduate programmes of the Scuola. The research structures of the two Faculties welcome students with a relevant study interest, enabling them to collaborate in a mature way with the activities of the researchers.

  • International

    The Scuola Normale is an institute of a decidedly international nature. Examinations for admission to the undergraduate degree course and for the PhD course are open to all citizens worldwide. A certain number of places on the PhD course are reserved for students from other countries. During the pre laurea and  post lauream teaching courses, study and research programmes are made available at overseas universities and research centres with which the Scuola forms an intense network of collaboration.  The doctorate course in particular is taught in a veritable graduate school in line with the highest international standards. 

Quantitative Finance group

The research activity of the group has the aim of using quantitative methods, both analytical and empirical, to investigate several aspects of financial markets at different time scales. The group has active collaborations with universities and research centers, banks, investment firms, IT companies, and market regulators.

The main research areas are:

- High frequency finance and market microstructure. The research is devoted to the mathematical modeling and empirical characterization of financial time series at high (transaction by transaction) and ultra-high (offers to buy and sell, limit order book) frequency. The areas of interest are liquidity modeling, price formation mechanisms, and optimal order execution. Finally the group investigates possible metrics of financial market instability at high frequency and the role of market structure on the high frequency properties of prices.

- Value investing and market efficiency. The group is working on an empirically based model of returns dynamics focusing on their evolution over a time horizon of fifteen - twenty years.  Aim of the approach is trying to answer Robert Shiller's question about returns of a stock index being predictable. We have collected empirical support to Shiller’s test of the appropriateness of prices in the stock market based on the Cyclically Adjusted Price Earning ratio, showing that it is a powerful predictor of future long run performances of the market. Other make use of Shannon entropy of symbolic time series to test efficient market hypothesis and more generally as measure of informational efficiency.

- Dependency between financial variables, correlation structures, and networks. By using techniques from multivariate statistics, data mining, and the theory of complex networks, we investigate and model the dependencies between financial variables, such as stock returns, Credit Default Swap returns, and trading activity of investors or brokerage firms. The objectives are to identify and model risk factors of an asset portfolio, to build more efficient estimators of covariance matrix for optimal portfolio allocation, and to build taxonomies of investors in order to study their mutual interaction.

- Systemic risk. The group is involved in researches on the mechanisms that might lead financial markets (or the whole economy) to an excessive risk of systemic events. This is done by using mathematical and computational models and empirical analyses. The considered entities are banks or investment firms, which invest in assets and are connected through credit networks. The mechanisms investigated as possible responsible of systemic risk are excessive leverage, positive feedback loops that amplifies small perturbations, and an excessive homogeneity among portfolios.

Head of the group: Fabrizio Lillo