The early years of the variance-gamma process

Abstract

Dilip Madan and I worked on stochastic process models with stationary independent increments for the movement of log-prices at the University of Sydney in the period 1980–1990, and completed the 1990 paper [21] while respectively at the University of Maryland and the University of Virginia. The (symmetric) Variance- Gamma (VG) distribution for log-price increments and the VG stochastic process first appear in an Econometrics Discussion Paper in 1985 and two journal papers of 1987. The theme of the pre-1990 papers is estimation of parameters of log-price increment distributions that have real simple closed-form characteristic function, using this characteristic function directly on simulated data and Sydney Stock Exchange data. The present paper reviews the evolution of this theme, leading to the definitive theoretical study of the symmetric VG process in the 1990 paper.