Skewed Normal Variance-Mean Models for Asset Pricing and the Method of Moments

Financial returns (log-increments) data, Y _t , t = 1,2,…, are treated as a stationary process, with the common distribution at each time point being not necessarily symmetric.
We consider as possible models for the common distribution four instances of the General Normal Variance-Mean Model (GNVM), which is described by Y | V ～ N ( a ( b + V ), c ²V + d² ) where V is a nonnegative random variable and a, b, c and d are constants. When V is Gamma distributed and d = 0, Y has the skewed Variance-Gamma distribution (VG). When V follows a Half Normal distribution and c = 0, Y has the well-known Skew Normal (SN) distribution. We also consider two cases where V is Exponentially distributed. Bounds for skewness and kurtosis in each case are found in terms of the moments of the V . These are useful in determining whether the Method of Moments for a given model is feasible. The problem of overdetermination of parameters via estimating equations is examined. 5 data sets of actual returns data, chosen because of their earlier occurrence in the literature, are analysed using each of the 4 models.