Organizzazione della Didattica


Computational finance


Corsi comuni


Frontali Esercizi Laboratorio Studio Individuale
ORE: 64 0 0 69


I anno1 semestre







Calendario Attività Didattiche



affine/integrativo Nessun ambitoSECS-P/059

Responsabile Insegnamento

Prof. CAPORIN MASSIMILIANOSECS-S/03Dipartimento di Scienze Statistiche

Altri Docenti

Prof. CAPORIN MASSIMILIANOIstituzionaleSECS-S/03Dipartimento di Scienze Statistiche

Attività di Supporto alla Didattica

Non previste


Elements of Economics and Mathematics of Financial Markets, elements of Statistics and Econometrics. Knowledge of the mean-variance approach of Markowitz, of the CAPM and APT models, and of the pricing of derivatives with binomial trees and with the Black and Scholes model.

The course, based on two modules, aims at providing to the students the ability to address computational problems and issues in the broad area of finance. Emphasis will be given to three core areas: asset allocation; risk management; derivative pricing. A the end of the course students will become advanced users of a statistical software enabling them to formalize and solve the computational problem related to an empirical finance question. The main module of the course will cover the formalization of computational problems into a statistical package. Both the main module and the minor (second module) will address real problems of computational finance by using the introduced software. Students of the degree in Statistics will follow the main module of the course and a dedicated second module that will discuss the basic topics of Financial Economics needed to understand the main module.

Theoretical lectures and empirical computer sessions.

Part 1: The formalization of computational problems into a statistical package - Introduction to the software; data management; basic tools for descriptive and graphical analyses; - Basic data manipulation tools; using already implemented functions; - Basic programming and how to write a batch file for execution; - Introduction to simulation methods: simulations from a given density; resampling/bootstrap from historical series; model-based bootstrap; - Further elements will be introduced during the course, when needed. Part 2: Asset Allocation - The classic approach, Markowitz's world: the efficient frontier with and without the risk-free asset and its empirical evaluation; - Markowitz in realistic applications: no short selling constraints, linear constraints, turnover constraints, inequality constraints, probabilistic constraints, cardinality constraints; empirical examples; the need of non-standard optimization approaches (mixed quadratic-integer programming and genetic algorithms); - The use of Markowitz in asset allocation programs and for strategic asset allocation; - Beyond Markowitz: from mean-variance, to mean-VaR; the optimization of alternative criterion functions; higher order portfolio allocation, is it worth? the modern approach of Risk Budgeting, implementation and examples; the information content of extreme market moves in the computation of the mean-variance matrix (the Chow-Kritzmann approach); is the historic efficient frontier fully reliable/the unique solution? Michaud’s simulation-based approach to the computation (and rebalancing) of efficient portfolios; - Investing for the long run: returns predictability and mean reversion; identification of optimal portfolios and simulation of wealth paths; Part 3: Risk Management and performance evaluation - The construction of simulated track records in allocation programs; methods and indicators for portfolio monitoring and performance evaluation; portfolio turnover and portfolios costs; - Indicators for the evaluation of portfolio risk (market risk, credit risk, systemic risk); some notes on operational risk; - The VaR and ES as methods for the evaluation of market risk; computing VaR and ES for one single position and at the portfolio level; historical approaches, model-based methods, simulation approaches, the use of copula functions; - Portfolio exposure to risk-factors: single-index and multifactor models; conditional factor models; models for market timing; VaR with risk-factors; Part 4: Pricing of derivatives and interest rates - Pricing in Black & Scholes world; replicating Black & Scholes by simulation; pricing of selected exotic options; - Pricing by simulation and time-series model-based methods; - Estimation of the interest rate zero curve by bootstrapping. The program might be subject to changes depending on a number of elements including: the interest of the students and their ability to solve computational problems with the statistical sowftare; the occurrence of particular events in the financial markets. Changes to the program content will affect the list of tasks included in the team work. The program above refers to both the main module and the second module of the course. For students in the degree of Statistics, the topics covered in the main module will be detailed at the befinning of the course. The second module will deal with the following topics: - Introduction to financial instruments and markets; - Investment choices under uncertainty and the approach of Markowitz; - Market equilibrium, CAPM and APT, and market efficiency; - Derivative pricing in discrete and continuous time.

The exam will be given in the form of a group homework. Each group (a team), will receive, at a beginning of the course (groups will be formed within the first two weeks of lectures), a list of tasks pointing at computational finance questions. The tasks list will be interated during the course. Each team will have to coordinate activities, inducing team members to interact. During the exam session, each team will show results in the form of a presentation (PowerPoint-like). Each team member must have full knowledge of the presentation and of the analyses performed by the team and of the main findings. For students of the degree in Statistics: the team work will include a shorter task list. The team work represents 65% of the final grade. The Financial Economnics module evaluation (35%) will be determined with a written exam.

The evaluation of the group homework will be based on the following criterias: - presence of appropriate answers to the various tasks assigned to the team; - appropriateness of the quantitative tools adopted by the team; - interpretation/economic intuition of the results obtained; - interaction across team members. For students of the degree in Statistics: the written exam might include both theoretical questions and empirical exercises based on the topics covered in the Financial Economics module.

Hull, J.C., Options, Futures and other derivatives. : Prentice Hall, Roncalli, T., Introduction to risk parity and budgeting. : Chapman & Hall, Bodie, Z., Kane, A. and Marcus, A.J., Investments. : McGraw Hill, Hull, J.C., Risk management and financial institutions. : Wiley Finance, Barucci, E., Marsala, C., Nencini, M., and Sgarra, C., Ingegneria finanziaria. : Egea, Elton, E.J., Gruber, M.J., Brown, S.J., and Goetzmann, W.N., Modern Portfolio Theory and Investment Analysis. : Wiley,

Lecture notes will be distributed to students Computer sessions and example codes will also be made available as well as the data sets used.