A barrier option is a path-dependent option
which is exterminated (knocked out) or initiated (knocked in) if the underlying spot price hits the specified barrier level during the life of the option.
(2017)  studied the pricing of vulnerable path-dependent options
using double Mellin transforms and obtained an explicit form pricing formula or semianalytic formula in each path-dependent option
This implies that the option is an ECC path-dependent option
with expected outflows, due to lapses, at fixed dates.
As Parisian option is a path-dependent option
like barrier option, the price depends on the path of an underlying asset as well as payoff at the maturity.
Things are more complicated in the case of exotic path-dependent option
such as Asian power options developed in this paper whose payoff depends on the geometric or arithmetic average of the underlying asset raised to power.
Things are more complicated in the case of path-dependent options
. The analytical solution of the pricing problem is not available and numerical approximations must be used.
It is one kind of path-dependent options
where the payoff is based on the maximum or the minimum of the underlying asset price during the drift of the option.
Asian options are a kind of common strong path-dependent options
, whose value depends on the average price of the underlying asset during the life of the option.
Linetsky, "Pricing and hedging path-dependent options
under the CEV process," Management Science, vol.
Kou, 1999, "Connecting Discrete and Continuous Path-Dependent Options
," Finance and Stochastics, 3, 55-82.
Yen, "Pricing discrete path-dependent options
under a double exponential jump-diffusion model," Journal of Banking and Finance, vol.
Chapter 15 looks at advanced derivative designs and strategies including portfolio insurance, customized products, and exotic options such as binary and path-dependent options
. Finally, the book ends with a chapter entitled "Financial Risk Management," which discusses the structure of the derivatives industry (d ealers) and miscellaneous issues, including accounting for derivatives.