6. Suitable Distributions for Returns

  1. Bernhard Pfaff

Published Online: 30 OCT 2012

DOI: 10.1002/9781118477144.ch6

Financial Risk Modelling and Portfolio Optimization with R

Financial Risk Modelling and Portfolio Optimization with R

How to Cite

Pfaff, B. (2012) Suitable Distributions for Returns, in Financial Risk Modelling and Portfolio Optimization with R, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781118477144.ch6

Author Information

  1. Invesco Global Strategies, Germany

Publication History

  1. Published Online: 30 OCT 2012
  2. Published Print: 28 DEC 2012

ISBN Information

Print ISBN: 9780470978702

Online ISBN: 9781118477144



  • fBasics;
  • financial market data;
  • generalized hyperbolic distribution (GHD);
  • generalized lambda distribution (GLD);
  • normal inverse Gaussian distributions (NIG);
  • R package;
  • return distribution;
  • risk modelling;
  • tail behaviour


The need to model not just the tail behaviour of losses, but the entire return distribution arises when, for example, returns have to be sampled for Monte Carlo type applications. This chapter presents the distribution classes that allow returns to be modelled in their entirety, thereby acknowledging the stylized facts. It introduces the distribution classes of the generalized hyperbolic distribution (GHD) and its special cases, namely the hyperbolic (HYP) and normal inverse Gaussian distributions (NIG), as well as the generalized lambda distribution (GLD). The chapter offers a synopsis of available R packages for the GHD, including fBasics and GeneralizedHyperbolic packages. The R packages for the GHD discussed in the chapter include Davies and lmomco packages. Finally, the chapter provides applications of the GHD, HYP, NIG and GLD to financial market data.

Controlled Vocabulary Terms

Functional programming and lambda calculus; Inverse Gaussian Distribution; risk analysis; Tail Area (Of A Distribution)