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Answer: The implied distribution has a heavier left tail and a heavier right tail.
B is correct. For a foreign currency option, the implied distribution gives a relatively high price for the option. The implied volatility is relatively low for at-the-money options, but it becomes higher as the option moves either in-the-money or out-of-the-money. Thus, the implied distribution has heavier tails than the lognormal distribution. **Key Points:** - The volatility smile pattern described (low at-the-money volatility, higher volatility for both in-the-money and out-of-money options) indicates that the market is pricing in higher probabilities of extreme price movements in both directions - This results in an implied distribution with fatter/heavier tails compared to the lognormal distribution assumed in Black-Scholes - Heavier tails mean higher probabilities of extreme price movements in both directions (left and right) - This pattern is commonly observed in foreign exchange markets where both large upward and downward movements are considered more likely than what the lognormal distribution would predict
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A risk analyst at an investment bank is examining the assumptions the bank uses in its foreign exchange (FX) option pricing model. Currently, the implied volatility in a particular FX pair is relatively low if an option is at-the-money and becomes progressively higher as the option moves either more in-the-money or more out-of-the-money. How does the distribution of option prices on this FX pair implied by the Black-Scholes-Merton model compare to a lognormal distribution with the same mean and standard deviation?
A
The implied distribution has a heavier left tail and a less heavy right tail.
B
The implied distribution has a heavier left tail and a heavier right tail.
C
The implied distribution has a less heavy left tail and a heavier right tail.
D
The implied distribution has a less heavy left tail and a less heavy right tail.
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