  The paper examines the Fractional Fourier Transform (FRFT) based technique as
tools for obtaining the probability density function and its derivatives; and
broadly for fitting stochastic model with the fundamental probabilistic
relationships of infinite divisibility. The probability density functions are
computed and the distributional proprieties such as leptokurtosis, peakedness,
and asymmetry are reviewed for Variance-Gamma (VG) model and Compound Poisson
with Normal Compounding model. The first and second derivatives of probability
density function of the VG model are also investigated. The VG model has been
increasingly used as an alternative to the Classical Lognormal Model (CLM) in
modelling asset price. The VG model with fives parameters was estimated by the
FRFT. The data comes from the SPY historical data, the SPDR S\&P 500 ETF (SPY).
The Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits better
the cumulative distribution of the sample data than the CLM. The best VG model
comes from the FRFT estimation.
