  Volume weighted average price (VWAP) options are a popular security type in
many countries, but despite their popularity very few pricing models have been
developed so far for VWAP options. This can be explained by the fact that the
VWAP pricing problem is set in an incomplete market since there is no
underlying with which to hedge the volume risk, and hence there is no uniquely
defined price. Any price, which is obtained will include a market price of
volume risk which must be determined from the corresponding volume statistics.
Our analysis strongly supports the hypothesis that the empirical volume
statistics of ASX equities can be described reasonably well by fitted gamma
distributions. Based on this observation we suggest a simple gamma
process-based model that allows for the exact analytic pricing of VWAP options
in a rather straightforward way.
