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Pricing asian options

It is considered "exotic" in the sense that the pay-off is a function of the underlying asset at multiple points throughout its lifetime, rather than just the value at expiry. An Asian option actually utilises the mean of the underlying asset price sampled at appropriate intervals as the basis for its pay-off, which is where the "path-dependency" of the asset comes from. The name actually arises because they were first devised in in Tokyo as options on crude oil futures. There are two types of Asian option that we will be pricing. They are the arithmetic Asian and the geometric Asian. They differ only in how the mean of the underlying values is calculated.
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Asian option

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Monte Carlo Asian Option Pricing in CUDA – Paws Development

An Asian option is an option type where the payoff depends on the average price of the underlying asset over a certain period of time as opposed to standard options American and European where the payoff depends on the price of the underlying asset at a specific point in time maturity. These options allow the buyer to purchase or sell the underlying asset at the average price instead of the spot price. Asian options have relatively low volatility due to the averaging mechanism. They are used by traders who are exposed to the underlying asset over some time, such as consumers and suppliers of commodities , etc. They are constructed by tweaking ordinary options in minor ways.
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All these methods involve some tradeoffs between numerical accuracy and computational efficiency. This example also demonstrates how variations in spot prices, volatility, and strike prices affect option prices on European Vanilla and Asian options. Asian options are securities with payoffs that depend on the average value of an underlying asset over a specific period of time. Underlying assets can be stocks, commodities, or financial indices.
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An Asian option or average value option is a special type of option contract. For Asian options the payoff is determined by the average underlying price over some pre-set period of time. This is different from the case of the usual European option and American option , where the payoff of the option contract depends on the price of the underlying instrument at exercise; Asian options are thus one of the basic forms of exotic options.
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