Chapter 8 - Modelling dependence with copulas and applications to risk management

Abstract

Integrated risk management (IRM) is concerned with the quantitative description of risks to a financial business. The qualitative aspects of IRM are extremely important. All quantitative models are based on assumptions vis-a-vis the markets on which they are to be applied. Standard hedging techniques require a high level of liquidity of the underlying instruments; prices quoted for many financial products are often based on “normal” conditions. The latter may be interpreted in a more economic sense, or more specifically referring to the distributional (i.e., normal, Gaussian) behavior of some underlying data. One of the main aims of this chapter is to present effective algorithms for random variate generation from the various copula families studied. The properties of the specific copula family are often essential for the efficiency of the corresponding algorithm. The chapter also provides a general algorithm for random variate generation from copulas.