Asset Return Distribution and Its Application to Gold Future Index

Abstract

Returns and probability distribution of log-returns
in the financial time series are crucial for further development of
quantitative finance. This paper suggests more appropriate
distribution for the gold future index by reviewing history of the
asset return distributions and documenting some stylized facts.
The return of the sample of daily 2364 observations is fitted to
different distribution. This identifies the Student’s t distribution
with about 4.4 degree of freedom as a typical estimated logreturn
distribution for Gold future index with significance level
of 1%. Test of the goodness of fit and log-likelihood values are
performed in order to quantitatively access the quality of the
estimation. Furthermore, this result can be interpreted as a
stylized fact with a high level of significance.