Insegnamento a.a. 2015-2016



Department of Finance

Course taught in English

Go to class group/s: 31
CLMG (6 credits - II sem. - OP  |  SECS-P/05) - M (6 credits - II sem. - OP  |  SECS-P/05) - IM (6 credits - II sem. - OP  |  SECS-P/05) - MM (6 credits - II sem. - OP  |  SECS-P/05) - AFC (6 credits - II sem. - OP  |  SECS-P/05) - CLAPI (6 credits - II sem. - OP  |  SECS-P/05) - CLEFIN-FINANCE (6 credits - II sem. - OP  |  SECS-P/05) - CLELI (6 credits - II sem. - OP  |  SECS-P/05) - ACME (6 credits - II sem. - OP  |  SECS-P/05) - DES-ESS (6 credits - II sem. - OP  |  SECS-P/05) - EMIT (6 credits - II sem. - OP  |  SECS-P/05)
Course Director:

Classes: 31 (II sem.)

Course Objectives

This course is designed to illustrate how multivariate techniques are applied to finance, with particular reference to market and credit risk measurement, as well as to the pricing of multi-asset derivatives. Market crashes and the resulting contagion effects have highlighted the limitations of linear correlation in capturing the dependence structure among financial asset returns for the purposes of: 1) assessing the risk of a financial institution; 2) pricing derivatives whose value depends on the interaction in the performance of different underlyings. Hence, it is essential to learn how to model dependence beyond the correlation structure implied by multivariate normal distributions. A number of practical applications to the pricing of equity / credit derivatives, to risk management, and to issues of structuring of complex derivative securities will be provided. A few sessions will be devoted to the practical implementation of models in MatLab.

Course Content Summary

  • Review of parametric multivariate modeling in financial econometrics with emphasis on dependence and correlations.
  • Tools from stochastic calculus: from deterministic to stochastic differential equations (SDEs), Brownian motions, stochastic integrals, martingales, driftless SDEs and semi-martingales, quadratic variation/covariation, solutions to general SDEs, Ito's formula and Stochatsic Leibniz rule.
  • Measures of dependence further to correlations and copulas.
  • Modeling default correlation (pricing): reduced form intensity models; structural models; single name credit derivatives (CDS); CDS bootstrap; multi name credit derivatives (CDOs); the CDO base and compound correlations; Gaussian Copula approach and extensions.
  • Risk Management (credit risk). Default correlation models: one-factor Gaussian and multi-factor Gaussian; applications to credit risk of a portfolio of loans.
  • Risk Management (market risk). Dependence structure in the Fundamental Review of the Trading Book approach, Sensitivity Based Approach. Applications to capital requirements and initial margin.
  • Introduction to structured financial instruments: equity protection structures; exotic options and barriers and their applications in structuring.
  • Correlations and structured products: basket derivatives and certifcates.

Detailed Description of Assessment Methods

There are two separate exam tracks, for attending vs. non-attending students, even though all students are invited to actively attend and participate to the lectures. Moreover, the structure of the exam for attending students reflects the three-part structure of the course (i.e., tools and risk management, pricing applications, structuring applications).

Track 1, for attending students: 1 hour written exam on entire syllabus and take-home project.

Track 2, for non-attending students: 2.5 hours written exam on entire syllabus.


Lecture notes and class presentations of the material should be taken as a guidance for further study on selected parts of the textbooks:
  • D. Brigo, F. Mercurio , Interest Rate Models Theory and Practice, with Smile, Inflation and Credit (2006), Springer Verlag.
  • P.F. Christoffersen , Elements of Financial Risk Management, Academic Press, (2012) 2nd edition (chapters 1-10, henceforth “Christoffersen”).
  • Il Sole 24 Ore , I certificati di investimento. Mercati, strutture finanziarie, strategie gestionali.M. Camelia (2009) (ed.) Edizioni Il Sole 24 ORE.
  • S. Shreve , Stochastic Calculus for Finance II, (2004) New York: Springer.
  • P. Wilmott , Paul Wilmott Introduces Quantitative Finance. (2007) John Wiley & Sons.
For each topic we will also provide suggestions for further reading, whose consultation is left to the students’ initiative.
Exam textbooks & Online Articles (check availability at the Library)


Good knowledge of mathematics (calculus and algebra), statistics, and time series econometrics is assumed. Although these are not formal pre-requisites, a working knowledge of the key contents of the courses in the Quantitative Finance and Derivatives (I and II) sequence may prove useful.

Last change 15/06/2015 11:07