An Asian option is a special form of an exotic option whose pay-off profile on exercising of the difference between the exercise price and the average of past prices as regards the underlying security is dynamic.
The main feature of Asian options is that the exercise date of the option value is not determined by the current price of the underlying asset, but on the average rates of particular terms specified.
Asian options are well suited for the securing of exchange rate risks, if a product is sold at a specified future date, various costs are incurred up to that time, and thus subject to a continuous exchange risk.
Asian options scale down the risk associated with market manipulation of the underlying instrument at maturity. And the relative cost of Asian options is much more appealing than that of European or American options, thanks to the averaging feature. The Asian options are also advantageous because they tend to cut down the volatility synonymous with the option.
An arithmetic Asian put option works similarly, only the payout X – \ bar (S), i.e. the exercise is then advantageous if the average of the course is below the exercise price X. As usual with options, the option holder is in a position to exercise his right to payment only if \ bar (S) – X is a positive amount.
A fundamental relationship between arithmetic and geometric option can be seen when the logarithmic value of the underlying asset, so l_t: = ln \ (S_t) computes. A geometric Asian call option on S with a base value X = 0 thus pays exactly the exponential of a corresponding arithmetic option that refers to the Basisiwert L rather than S. This property can be advantageous, as in many financial mathematical models of the logarithms of the course is easier to handle than the course itself.
It is possible to efficiently implement the Variance Gamma model when pricing Asian style options, and proceed to generating the model’s procedure using the Bondesson series representation.
The expected value of the payout with respect to calculation of probability measure, can be derived even for the Asian options. However, it is very difficult as this can mean for example in three years, and daily observation, the calculation of an average of over a thousand inter-dependent random variables. In such cases, it often helps to use a Monte Carlo simulation to estimate the expected value.