  The paper examines the Fractional Fourier Transform (FRFT) based technique as
a tool for obtaining the probability density function and its derivatives, and
mainly for fitting stochastic model with the fundamental probabilistic
relationships of infinite divisibility. The probability density functions are
computed, and the distributional proprieties are reviewed for Variance-Gamma
(VG) model. The VG model has been increasingly used as an alternative to the
Classical Lognormal Model (CLM) in modelling asset prices. The VG model was
estimated by the FRFT. The data comes from the SPY ETF historical data. The
Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits the
cumulative distribution of the sample data better than the CLM. The best VG
model comes from the FRFT estimation.
