A note on the estimation of a Gamma-Variance process: Learning from a failure

This paper con?rms that, as originally reported in Seneta (2004, p. 183), it is impossible to replicate Madan et al.?s (1998) results using log daily returns on S&P 500 Index from January 1992 to September 1994. This failure leads to a close investigation of the computational problems associated with ?nding maximum likelihood estimates of the parameters of the popular VG model. Both standard econometric software, such as R, and non-standard optimization software, such as Ezgrad described in Tucci (2002), are used. The complexity of the log-likelihood function is studied. It is shown that it looks very complicated, with many local optima, and may be incredibly sensitive to very small changes in the sample used. Adding or removing a single observation may cause huge changes both in the maximum of the log-likelihood function and in the estimated parameter values.