# Path-dependent option

## Path-dependent option

An option whose value depends on the sequence of prices of the underlying asset rather than just the final price of the asset.

## Path Dependent Option

An option contract whose price is determined according to some formula involving the price of the underlying asset over time. Most options have prices that are dependent upon the value of the underlying asset at the time the option is exercised. A path dependent option, on the other hand, uses a more complex formula. For example, in some Asian options, the strike price is the average of the prices of the underlying asset over the life of the contract.
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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

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