  This paper explores the theory behind the rich and robust family of
{\alpha}-stable distributions to estimate parameters from financial asset
log-returns data. We discuss four-parameter estimation methods including the
quantiles, logarithmic moments method, maximum likelihood (ML), and the
empirical characteristics function (ECF) method. The contribution of the paper
is two-fold: first, we discuss the above parametric approaches and investigate
their performance through error analysis. Moreover, we argue that the ECF
performs better than the ML over a wide range of shape parameter values,
{\alpha}{\alpha} including values closest to 0 and 2 and that the ECF has a
better convergence rate than the ML. Secondly, we compare the t location-scale
distribution to the general stable distribution and show that the former fails
to capture skewness which might exist in the data. This is observed through
applying the ECF to commodity futures log-returns data to obtain the skewness
parameter.
