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ADVANCED TOPICS IN FINANCE AND INSURANCE

Syllabus

EN IT

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.


Prerequisites

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).

Program

The course consists on two main topics:
I) Financial Engineering for Investment (3 weeks). This module covers valuation across instruments and asset classes:
- Valuation across financial instruments, including linear pricing theory foundations, risk-neutral valuation for derivatives.
- Identification, modeling and forecasting of key risk drivers for the returns of equities, fixed income, derivatives, credit, high frequency, foreign exchange
- Repricing techniques: Monte Carlo full repricing, analytical Greeks approximations.
II) Data Science for Finance. This module covers the statistical tools needed to model and estimate the joint dynamics of the markets:
- Multivariate distributions and notable classes: elliptical, exponential, discrete
- The “mean-covariance/linear” ecosystem: mean vector, covariance matrix, ellipsoid, affine equivariance, correlation, linear prediction
- Estimation of the “mean-covariance/linear” ecosystem: historical, maximum likelihood, Bayesian, random matrix theory and shrinkage
- Linear factor models: regression, principal component analysis, factor analysis, cross-sectional models
- Machine learning models; Feature engineering and enhancements: feature bases, trees, neural networks, gradient boosting, lasso/ridge regularization, random forests, etc.

Books

Multi-channel E-textbook ARPM Lab

Bibliography

A. Meucci, Risk and Asset Allocation, Springer 2009

Teaching methods

The course is attended by students according to the program indicated weekly by the teachers. In addition, each week there is a classroom lesson with teachers during which a series of exercises are proposed for students, possibly divided into small groups, to solve and discuss (flipped classroom).

Exam Rules

The learning assessment is based on three criteria:

1) active participation in the ‘flipped classroom’ activities. 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 test, in “open book” mode, consists of open-ended questions. 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.
The score of th examination test is expressed in thiertieths according to the following criteria:
o Unsuitable: significant deficiencies and/or inaccuracies in knowledge and understanding of the topics; limited capacity for analysis and synthesis, frequent generalizations.
o 18-20: barely sufficient knowledge and understanding of the topics with possible imperfections; sufficient capacity for analysis, synthesis and autonomy of judgement.
o 21-23: Routine knowledge and understanding of the topics; Correct analysis and synthesis skills with coherent logical argumentation.
o 24-26: Fair knowledge and understanding of the topics; good capacity for analysis and synthesis with rigorously expressed arguments.
o 27-29: Comprehensive knowledge and understanding of the topics; Considerable ability to analyze, synthesize. Good autonomy of judgement.
o 30-30L: Excellent level of knowledge and understanding of the topics. Remarkable analytical and synthetic skills and independent judgement. Arguments expressed in an original manner.