Some New Bivariate IG and NIG-Distributions for Modelling Covariate Financial Returns

30 Pages Posted: 28 Mar 2007

See all articles by Jostein Lillestol

Jostein Lillestol

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: January 8, 2007

Abstract

The univariate Normal Inverse Gaussian (NIG) distribution is found useful for modelling financial return data exhibiting skewness and fat tails. Multivariate versions exists, but may be impractical to implement in finance. This work explores some possibilities with links to the mixing representation of the NIG distribution by the IG-distribution. We present two approaches for constructing bivariate NIG distribution that take advantage of the correlation between the univariate latent IG-variables that characterizes the marginal NIG-distribution. These are readily available from the marginal estimation, either by maximum likelihood via the EM-algorithm or by Bayesian estimation via Markov chain Monte Carlo methods. A context for implementation in finance is given.

Keywords: Financial returns, bivariate distribution, NIG distribution, mixture representation, inverse Gaussian distribution, bivariate simulation

Suggested Citation

Lillestol, Jostein, Some New Bivariate IG and NIG-Distributions for Modelling Covariate Financial Returns (January 8, 2007). NHH Dept. of Finance & Management Science Discussion Paper No. 2007/1, Available at SSRN: https://ssrn.com/abstract=971557 or http://dx.doi.org/10.2139/ssrn.971557

Jostein Lillestol (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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