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.

Efficient procedures for valuing European and American path-dependent options.

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.

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.

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.

This implies that the option is an ECC path-dependent option with expected outflows, due to lapses, at fixed dates.

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