20263 - ADVANCED TOOLS FOR RISK MANAGEMENT AND ASSET PRICING (CORRELATION AND DEPENDENCE MODELLING)

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 multiasset 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: assessing the risk of a financial institution; 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 and to risk management is provided. Ample time is devoted to the practical implementation of models during MatLab sessions. Some of the applications are illustrated by leading practitioners in the field.

• A review of the basics of multivariate modelling in finance: multivariate normal distribution; standard estimators of covariance and correlation; dimension reduction techniques. The pitfalls of assumption of multivariate normal returns.
• Alternative measures of dependence in finance.
  • Rank correlations; tail dependence-market crashes and contagion.
  • Copulas and dependence: basic properties and copulas; Gaussian and Archimedean copulas; fitting copulas to empirical financial data.
• Application 1: Modelling default correlation.
  • A review of default models (structural and intensity-based).
  • Single-name credit derivantes (Credit Default Swaps).
  • Defaut correlation models: one-factor Gaussian model and its extensions.
  • Pricing and hedging of structured credit products (basket default swaps, CDO).
• Application 2: Risk management.
  • Dependence structures in financial risk management: VaR and beyond.
  • Contagion-risk measures.
  • Counterparty risk measures.
  • Risk aggregation.
• Application 3: Pricing equity/currency multiasset derivatives.

Student evaluation consists of both an empirical assignment and a final written closed-book exam. The empirical assignment accounts for 30% of the overall mark, while the written exam accounts for 70% of the overall mark.
The empirical assignment may be produced either by individuals or by groups of students composed by up to four people. The mark gained in the empirical assignment remains valid for one academic year.
Non attending students have the option to take only a written exam. In this case, the written exam is longer and more comprehensive than the written exam for students who opt for the combination assignment + written exam, and accounts for 100% of the overall mark.

• The course material includes academic papers, slides and other notes that are made available on yoU@B.
• The following chapters from: A.J. MECNEIL, R.FREY, P. EMBRECHTS, Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University Press, 2005, can be beneficial for a better understanding of the first part of the course (parts 1 and 2): Chapters 2,3 (3.1, 3.2 - example 3.7-, 3.3.3 only), 4 (4.1 only), 5 (5.1.1, 5.1.2, 5.1.3, 5.1.4, 5.2, 5.3.1, 5.3.2, 5.5.1, 5.5.3 only), 6 (6.1.1, 6.1.2, 6.1.3 only).

Students are expected to have attended a core course in statistics and to have good familiarity with undergraduate calculus and linear algebra. Prior exposure to financial derivatives (options, swaps) is beneficial, although not essential.