Nonparametric risk management with generalized hyperbolic distributions

Abstract

In this article we propose the generalized hyperbolic adaptive volatility (GHADA) risk management model based on the generalized hyperbolic (GH) distribution and on a nonparametric adaptive methodology. Compared with the normal distribution, the GH distribution has semiheavy tails and represents the financial risk factors more appropriately. Nonparametric adaptive methodology has the desirable property of being able to estimate homogeneous volatility over a short time interval and reflects a sudden change in the volatility process. For the German mark/U.S. dollar exchange rate and German bank portfolio data, the proposed GHADA model provides more accurate Value at risk calculations than the models with assumptions of the normal and t distributions. © 2008 American Statistical Association.