  In this paper we extend Buchen's method to develop a new technique for
pricing of some exotic options with several expiry dates(more than 3 expiry
dates) using a concept of higher order binary option. At first we introduce the
concept of higher order binary option and then provide the pricing formulae of
$n$-th order binaries using PDE method. After that, we apply them to pricing of
some multiple-expiry exotic options such as Bermudan option, multi time
extendable option, multi shout option and etc. Here, when calculating the price
of concrete multiple-expiry exotic options, we do not try to get the formal
solution to corresponding initial-boundary problem of the Black-Scholes
equation, but explain how to express the expiry payoffs of the exotic options
as a combination of the payoffs of some class of higher order binary options.
Once the expiry payoffs are expressed as a linear combination of the payoffs of
some class of higher order binary options, in order to avoid arbitrage, the
exotic option prices are obtained by static replication with respect to this
family of higher order binaries.
