Following an introduction to the key concepts of probability, statistics, econometrics, financial engineering, and institutions in the financial intermediation markets, the course introduces emerging aspects of market, credit and liquidity risk.
In the field of credit risk, the primary objective of the Master’s is to provide skills in the analysis of so-called “big data”, or rather the enormous amount of data that financial institutions have to deal with. The practical focus of the training course is implemented through the use of the most common computing techniques used by financial institutions in order to help Master’s students enter the world of work.

Indicatively the lectures will be held from Monday to Thursday from 10:00 to 16:30, with up to 20 hours a week of classes via live streaming.
Furthermore, for some courses a blended learning approach will be used: students will be able to choose to follow lessons either remotely or in the classroom.

  • Subjects

Statistics: Michele Costa

  • Statistical analysis of financial variables: mean-variance analysis and portfolio
  • Linear models: market model and CAPM
  • Inference: parameter estimation, hypothesis testing and residual analysis

Financial econometrics: Luca De Angelis, Luca Fanelli

  • Stylized facts of return distributions
  • Random walk model and efficient market hypothesis
  • Asset pricing: intertemporal equilibrium, puzzles
  • VAR-based approach to present-value model

Volatility modelling: Giuseppe Cavaliere, Anders Rahbek

  • ARCH and GARCH-type models
  • Maximum likelihood estimation
  • Volatility forecasting
  • Realized volatility and high-frequency data analysis

Programming: Fabio Gobbi, BID Company

  • Introduction to SAS
  • Programming in R

Probability: Sabrina Mulinacci

  • Probability spaces
  • Random variables, moments, main distributions
  • Random vectors, multivariate distributions
  • Copulas

Financial calculus: Luca Vincenzo Ballestra

  • Deterministic discount and capitalization factors
  • Stochastic processes: Brownian motion, processes with independent increments, martingales
  • Stochastic integration
  • Stochastic differential calculus: Itô’s Lemma
  • Change of measure: exponential martingale and Girsanov’s theorem
  • EDS and PDE: geometric Brownian motion, Feynman-Kac’s theorem

Modelling of stock and (fixed) income markets: Silvia Romagnoli

  • No arbitrage assumption and fundamental theorems
  • Derivatives (stock market): Pricing and hedging in discrete time (binomial and trinomial model), and in continuous time (Black-Scholes, Ito's market, Black, multieconomy products)
  • Fixed income market: fundamentals equations implied by no-arbitrage assumption
  • Factor models: exponential affine models (Vasicek, Ho-Lee, CIR)
  • From HJM and BGM models to Market Model (FLMM, FSMM)

Financial intermediation: Giuseppe Torluccio

  • The Nature and Variety of Financial Intermediation
  • The What, How, and Why of Financial Intermediaries
  • Banks’ balance sheet and income structure
  • Identification and Management of Major Banking Risks
  • Spot Lending and Credit Risk
  • The Funding of the Bank
  • Bank Capital Structure
  • Securitization
  • Banks and markets
  • Comparative banking markets

Financial regulation: Andrea Resti, Francesco Cannata

  • The Bank Recovery and Resolution Directive: main contents and implications for financial risk management
  • Open issues in bank regulation: expected developments and possible pitfalls
  • Banking and financial supervision: framework and developments
  • Regulatory and supervisory issues: the state of the art  

Market risk: Sabrina Mulinacci, Gian Luca Tassinari

  • Risk measures: VaR; coherent, convex and spectral risk measures
  • Risk exposures and sensitivity analysis
  • Risk reporting and cash flow mapping
  • Profit and loss distribution: parametric models
  • Profit and loss of nonlinear products: Monte Carlo methods
  • Non normal returns: historical simulation
  • Spread risk

Credit risk: Fabio Gobbi, Gian Luca Tassinari, Stefano Bonini

  • Single name credit risk: structural models
  • Single name credit risk: intensity based models
  • Double stochastic models
  • Models for the recovery rate
  • Credit derivatives and implied default probabilities
  • Multivariate credit derivatives
  • Multivariate default distributions and copula functions
  • Securitization structures and CDO markets
  • Counter party risk in derivatives: CVA and DVA
  • Credit risk mitigation: CSA and central clearing registers
  • Liquidity risk: funding and liquidity risk

Credit scoring: Gabriele Soffritti

  • Statistical methods for credit scoring based on

       - Logistic regression analysis

       - Discriminant analysis

       - Classification trees

Big data in risk management: Andrea Guizzardi, Silvia Romagnoli, Fabio Palladin, Sergio Pastorello, Enzo D’Innocenzo

  • Short term forecasting with machine learning techniques
  • Model complexity, data structures and forecasting performances
  • The comparisons of rival model under different risk aversion profiles
  • Clustering algorithms for data set complexity reduction
  • Combinatory copula-based models for financial risk management
  • Resampling methods: cross-validation e bootstrap
  • Model selection: Subset selection, LASSO, RIDGE ed estensioni, principal component regression e partial least squares
  • Methods based on regression trees: Bagging, Random Forest e Boosting
  • Support Vector Machines
  • Neural Networks