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Learning Objectives

LEARNING OUTCOMES: Learning of the main mathematical/statistical techniques used in the modeling and analysis of financial markets and in the measurement and management of risk.

KNOWLEDGE AND UNDERSTANDING: Students acquire knowledge of the main mathematical and statistical methods used for the analysis of financial markets. Alongside the more purely modeling aspects, application aspects are introduced through the use of dedicated software in multiple case studies.

APPLYING KNOWLEDGE AND UNDERSTANDING: At the end of the learning path the students are able to apply the acquired knowledge and techniques for the analysis of numerous financial products and risk measurement and management, also through the implementation of the presented techniques by means of programming languages.

MAKING JUDGEMENTS: The course aims to provide a broad and coherent view of the various aspects concerning risk analysis and management that can guide decisions and problem solving in financial contexts characterized by information that is often limited and rapidly evolving.

COMMUNICATION SKILLS: The student must be in possession of adequate knowledge that allows him to communicate clearly, to specialist and non-specialist interlocutors, the theoretical context of reference, and summarize the empirical evidence concerning the decisional problem raised in the financial framework.

LEARNING SKILLS: The student must be able to deal with the problems of analyzing complex financial products, risk measurement and management, and the necessary updating of knowledge and models in continuous evolution in the financial market in a largely autonomous way.


Basic knowledge of general mathematics (matrices and vectors, series, limits, continuity, derivatives, integrals), probability (random variables, distribution and density functions, expected values) and of the main financial products (shares, bonds and derivatives).


The course is based on the ARPM Quant Marathon. The main topics cover

I) Financial Engineering for Investment. This module covers valuation across instruments and asset classes:
- the standard financial engineering materials on risk-neutral valuation for derivatives (Black-Scholes, martingales, etc.)
- non-linear actuarial pricing (distortion measures, risk premium arguments, etc.)
- company/deal valuation, typically more tied to the investment banking and strategic consulting professions (discounted cash flows, comparable analysis, etc.).
II) Data Science for Finance. This module covers the statistical tools needed to model and estimate the joint dynamics of the markets.


On-line ARPM Lab platform


A. Meucci, Risk and Asset Allocation, Springer 2009

Teaching methods

The course is attended online by students through the ARPM platform according to the program indicated weekly by the teachers. Furthermore, every week there is a meeting in the classroom with the teachers on the program (flipped classroom) and a set of exercises are proposed that the students must solve and submit in electronic format.

Exam Rules

The learning assessment is based on three criteria:

1) attendance to the weekly flipped classrooms. Students divided into small groups are offered themes/problems to be addressed/solved within a given time to discuss with the rest of the class.
2) Delivery of homeworks. Every week there are problems that students must solve and submit in electronic format.
3) Final written test. The final exam consists of two/three open-ended, "open book" questions on each of the modules into which the program is divided, "Financial Engineering for Investment" and "Data Science for Finance." The questions include theoretical/modeling questions and problem-solving/examples addressed during the course. The student is expected to understand the main mathematical/statistical techniques used in financial market modeling and analysis and their subsequent independent application to complex financial products for risk measurement and management. In addition, communication skills in terms of language properties and clarity of exposition are assessed in adherence with the Dublin descriptors.