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.
Proof: Since Asian power option is path-dependent option whose price is related to path factor besides time and the underlying asset.
The pricing of European path-dependent option can always be implemented using the simple and efficient Monte Carlo simulation.
This implies that the option is an ECC path-dependent option with expected outflows, due to lapses, at fixed dates.
Their model is general enough to deal with any complex final payoff generated by European path-dependent options.
Specifically, the Quanto Asian Put belongs to the class of the path-dependent options.
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.
Kou, 1999, "Connecting Discrete and Continuous Path-Dependent Options," Finance and Stochastics, 3, 55-82.
Yamamoto, 2005, "A Double-exponential Fast Gauss Transform Algorithm for Pricing Discrete Path-dependent Options," Operations Research, vol.
The augmented state variable approach for pricing strongly path-dependent options
using either partial differential equations or Monte Carlo simulation
Chapter 15 looks at advanced derivative designs and strategies including portfolio insurance, customized products, and exotic options such as binary and path-dependent options
Pricing Path-Dependent Options
in a Backward Algorithm