Modeling Portfolios with Leptokurtic and Dependent Risk Factors

Recently, an approach to modeling portfolio distribution with risk factors distributed as Gram-Charlier (GC) expansions of the Gaussian law, has been conceived. GC expansions prove effective when dealing with moderately leptokurtic data. In order to cover the case of possibly severe leptokurtosis, the so-called GC-like expansions have been devised by reshaping parent leptokurtic distributions by means of orthogonal polynomials specific to them. In this paper, we focus on the hyperbolic-secant (HS) law as parent distribution whose GC-like expansions fit with kurtosis levels up to 19.4. A portfolio distribution has been obtained with risk factors modeled as GClike expansions of the HS law which duly account for excess kurtosis. Empirical evidence of the workings of the approach dealt with in the paper is included.