An option is a contract beetwen an option holder and an option writer that gives the owner the right to buy or sell an underlying asset at a pre-aggred strike price.
A standardized options, also known as plain vanilla options, are options with standardized contract and are regulary traded on stock exchanges, which ensure buyers and sellers of options greater liquidity. Example of such options are a straight call or put, either American or European options. On the other hand, there are exotic options that are not standardized and are mostly traded on over-the-counter markets (OTC).
Asian options are classified as exotic options. Their basic characteristic is that the value depends on the average price of the underlying instrument over a certain period. Often, the average price is calculated from the prices during the times that are precisely specified in the contract. Such options are very popular on the market since the averaging ensure the investor a payout that is less risky then plain vanilla options.
There are numerous permutation of asian options. The most basic are asian options with fixed strike and asian options with floating strike.
The average may be obtained in many ways. It can be arithmetic or geometric.
Pricing and hedging Asian options is difficult especially for options depending on arithmetic averaging. Generally, closed-form solutions do not exist and, thus, a variety of numerical pricing tehniques have been proposed.
In this paper we use the two-dimensional PDE introduced by Barraqund and Puddet (1996) to price Asian options using the Black - Sholes model. For efficency, we use exponential time integration (ETI) with dimensional splitting strategy.
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