Scandinavian Working Papers in Business Administration

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2007/1: Some new bivariate IG and NIG-distributions for modelling covariate nancial returns

Jostein Lillestøl ()
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Jostein Lillestøl: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway

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

JEL-codes: C10; C11; C13; C15; C16

29 pages, January 8, 2007

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