“…However, in recent years, the growth of barrier options has slowed down compared to the fast growth in the early 2000's (see, for example, the report of the Bank for International Settlements (2015) which documents the overall market movements). Nonetheless, new financial innovations related to barrier options continue to be introduced, as shown in Lei (2015). A Parisian option is also a barrier-type option in which its payment is activated (or deactivated) only if the underlying asset consecutively remains below (or above) a given barrier over a certain amount of time, namely the option window, specified in the contract.…”