An arithmetic Asian option in which the payoff is determined with respect to the arithmetic average price of the underlying asset over the lifespan of the call option. The method of averaging in an arithmetic Asian option takes into consideration the arithmetic average of the price of the underlying in calculating the payoff. The payoff could be either the positive difference between arithmetic average of underling price and exercise price, or zero.
Payoff = max [0, arithmetic average of underlying price – exercise price]
For example, on a given day, an investor bought a 60-day arithmetic call option on XYZ share. The exercise price of the call is $20 and the payoff is determined based on the arithmetic average price of the underlying share as established every time at the end of a period of 30 days. If the share price on the 30th and 60th day of the option’s term was $21 and $23, respectively, then the option’s payoff is:
Payoff = max [0, (21 + 23)/2 – 20] = $2
The payoff per contract is: 2 × 100 = $200
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