A Short Note on the Efficient Implementation of the NIG Distribution

The family of NIG distributions is a special case of the generalised hyperbolic distributions (Barndorff-Nielsen [1]). Due to their specific characteristics, NIG distributions are very interesting for applications in finance - they are a generally flexible four parameter distribution family that can produce fat tails and skewness, the class is convolution stable under certain conditions and the cumulative distribution function, density and inverse distribution functions can still be computed sufficiently fast. The distribution has been employed, e.g., for stochastic volatility modelling (Barndorff-Nielsen [2]). We have employed the NIG distribution for pricing of synthetic CDOs (see Kalemanova [4]). NIG distribution usually does not belong to the package of standard distributions that are already implemented in programs like Matlab, S-Plus, R and Mathematica. We have received numerous questions on the implementation of NIG from the readers of our paper. So we decided to write this short note on the efficient implementation of this distribution in Matlab.     «

The family of NIG distributions is a special case of the generalised hyperbolic distributions (Barndorff-Nielsen [1]). Due to their specific characteristics, NIG distributions are very interesting for applications in finance - they are a generally flexible four parameter distribution family that can produce fat tails and skewness, the class is convolution stable under certain conditions and the cumulative distribution function, density and inverse distribution functions can still be computed suf...     »