  This article is the second one in a series on the use of scaling invariance
in finance. In the first article (cond-mat/9906048), we introduced a new
formalism for the pricing of derivative securities, which focusses on tradable
objects only, and which completely avoids the use of martingale techniques. In
this article we show the use of the formalism in the context of path-dependent
options. We derive compact and intuitive formulae for the prices of a whole
range of well known options such as arithmetic and geometric average options,
barriers, rebates and lookback options. Some of these have not appeared in the
literature before. For example, we find rather elegant formulae for double
barrier options with moving barriers, continuous dividends and all possible
configurations of the barriers. The strength of the formalism reveals itself in
the ease with which these prices can be derived. This allowed us to pinpoint
some mistakes regarding geometric mean options, which frequently appear in the
literature. Furthermore, symmetries such as put-call transformations appear in
a natural way within the framework.
