Explanation:
This question describes a volatility smile pattern where implied volatility is higher for both deep in-the-money and deep out-of-the-money options compared to at-the-money options. This pattern is characteristic of leptokurtic distributions (fat-tailed distributions).
Volatility Smile Pattern: When implied volatility increases for both ITM and OTM options, it indicates that the market expects more extreme price movements than what a lognormal distribution would predict.
Distribution Characteristics:
Black-Scholes-Merton Assumption: The BSM model assumes lognormal distribution of asset prices, but the observed volatility smile indicates this assumption is violated.
Correct Answer Analysis:
Therefore, the implied distribution has both heavier left and right tails compared to a lognormal distribution with the same mean and standard deviation.
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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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