Despite numerical procedures often supply
a necessary accuracy, closed-form
expressions allow to escape any accumulation of errors. In this paper we discuss the possibility
of obtaining explicit results for a variance gamma process. The
exact distribution of the maximum of the variance gamma process over a finite interval of time
is derived. The prices of path-dependent options including digital
barrier, fixed-strike lookback and lookback options are established.
The obtained formulas are based on values of hypergeometric
functions.