  The method and characteristics of several approaches to the pricing of
discretely monitored arithmetic Asian options on stocks with discrete, absolute
dividends are described. The contrast between method behaviors for options with
an Asian tail and those with monitoring throughout their lifespan is
emphasized. Rates of convergence are confirmed, but greater focus is put on
actual performance in regions of accuracy which are realistic for use by
practitioners. A hybrid approach combining Curran's analytical approximation
with a two-dimensional finite difference method is examined with respect to the
errors caused by the approximating assumptions. For Asian tails of equidistant
monitoring dates, this method performs very well, but as the scenario deviates
from the method's ideal conditions, the errors in the approximation grow
unfeasible. For general monitoring straightforward solution of the full
three-dimensional partial differential equation by finite differences is highly
accurate but suffers from rapid degradation in performance as the monitoring
interval increases. For options with long monitoring intervals a randomized
quasi-Monte Carlo method with control variate variance reduction stands out as
a powerful alternative.
