I know Asian option is defined as follow $$\left(\frac{1}{T}\int_{0}^{T}S_t dt-K\right)^+$$ Is there a good idea behind this definition.
Thanks.
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$\begingroup$ en.wikipedia.org/wiki/Asian_option. $\endgroup$– user16651Commented Aug 2, 2016 at 20:18
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2$\begingroup$ Where did you get this definition from? I doubt you'll ever see something like this in reality, since the continuous integral is going to be very difficult for two parties to agree on. It'll be discrete, based on agreeable fixings (ie close prices). $\endgroup$– willCommented Aug 2, 2016 at 20:19
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1$\begingroup$ This type of option probably may only be found in textbooks. $\endgroup$– GordonCommented Aug 2, 2016 at 20:37
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1$\begingroup$ @noob2 you see them in Fx too. I've seen all three forms of mean in there too (arithmetic, geometric, and harmonic). Always discrete though, never continuous. $\endgroup$– willCommented Aug 2, 2016 at 22:17
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1$\begingroup$ The continuous average may be used as an approximation for daily arithmetic averages. $\endgroup$– GordonCommented Aug 3, 2016 at 12:46
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1 Answer
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This is the standard textbook definition for the payoff of an arithmetic average Asian call option.
In reality the average will be based on a daily average of stock prices over some period at the end of the life of the option.
The first "idea" behind Asian options is that the payoff is harder to manipulate by dealers - the story is that in certain small markets dealers were able to push down the stock price at expiry by selling shares and so move options out of the money. If the final payoff is based on an average then this is harder to achieve.
The second "idea" is that the volatility of the average of the stock price is lower than the volatility of the stock price. This makes the option cheaper and so more attractive to investors who believe that the stock price will rise.
