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) [25] 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.
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.