FRM Part I · FRM Exam Part I · Exotic Options
Compared with an otherwise identical standard European call option, an arithmetic-average-price Asian call option on the same underlying and strike typically has which characteristic?
The Asian call typically has a lower premium than the standard European call. Averaging smooths the price path, so the average has lower volatility than the terminal price. Since option value increases with volatility, the Asian option is cheaper.
- AA lower premium, because averaging reduces the volatility of the underlying value used in the payoffCorrect
- BA higher premium, because averaging increases the chance of a large payoff
- CThe same premium, because averaging does not affect the expected payoff
- DA higher premium, because the holder can choose the best averaging date
Explanation
Averaging prices over time reduces the variance of the settlement value relative to the terminal price alone. Lower effective volatility lowers option value, so the Asian call is cheaper. The option does not allow choosing dates, and the averaging does change option value even though it affects the forward-looking expected value only slightly.
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