Financial risk management with normal inverse Gaussian distributions

Abstract

In this study we investigate using normal inverse Gaussian distribution(NIG) in financial risk management. The first step in risk management is to find a correct model for evaluation of financial asset. Commonly asset returns are assumed to be normally distributed. However, we observed from empirical financial data that asset returns have distributions with fat tails and that they are often skew. In this paper we consider the normal inverse Gaussian distribution to model the log returns of financial data. The NIG family has the nice properties that it is flexible and the parameters can be solved closed form. These distributions allow representation of the skew distributions and tails tent to be heavier than those of the normal. The moments of NIG distributions are important in VaR calculations and derivative pricing. The financial risks associated with single securities and the portfolio investments are measured with VaR and Expected Shortfall. We estimate VaR and Expected Shortfall for the fitted Gaussian distribution and normal inverse Gaussian distribution. Then results that obtained both of them are compared. We show that the NIG model provides a potentially flexible framework to model the marginal distribution of asset returns. Finally we use the simulated data to show the performance of model. © EuroJournals Publishing, Inc. 2010.