  In this paper the Buchen's pricing formulae of (higher order) asset and bond
binary options are incorporated into the pricing formula of power binary
options and a pricing formula of "the normal distribution standard options"
with the maturity payoff related to a power function and the density function
of normal distribution is derived. And as their applications, pricing formulae
of savings plans that provide a choice of indexing and discrete geometric
average Asian options are derived and the fact that the price of discrete
geometric average Asian option converges to the price of continuous geometric
average Asian option when the largest distance between neighboring monitoring
times goes to zero is proved.
