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Answer: The implied volatility smile commonly seen in equity options is due to the higher probability of a greater than three standard deviation price change than would be expected if prices are lognormally distributed.
## Explanation **Option A is correct** because: - Equity options typically exhibit a **volatility smile** where implied volatility is higher for deep out-of-the-money puts and calls - This pattern reflects market participants' perception that **extreme price movements** (greater than 3 standard deviations) occur more frequently than predicted by the lognormal distribution assumption in the Black-Scholes model - The higher probability of large price changes is often attributed to factors like market crashes, earnings surprises, or other significant corporate events **Option B is incorrect** because: - Foreign exchange rate options typically exhibit a **volatility smile** that is more symmetric - The smile in FX options is primarily driven by the **leptokurtic nature** of exchange rate returns (fat tails), meaning extreme movements in both directions occur more frequently than expected - The pattern is not specifically concentrated in the 1-2 standard deviation range, but rather affects the entire distribution, particularly the tails **Key Differences Between Equity and FX Volatility Smiles:** - **Equity options**: Often show an asymmetric smile/skew with higher implied volatility for OTM puts (reflecting crash risk) - **FX options**: Typically show a more symmetric smile due to the two-sided nature of currency movements - Both reflect deviations from the lognormal distribution assumption, but for different underlying reasons related to their respective market dynamics
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An option pricing analyst has been asked to write a report examining the relationship between option prices and implied volatility curves. The analyst notes that the implied volatility curves of different underlying assets often have different shapes and explains the reasons why this occurs. Which of the following statements can correctly be included in the report?
A
The implied volatility smile commonly seen in equity options is due to the higher probability of a greater than three standard deviation price change than would be expected if prices are lognormally distributed.
B
The implied volatility smile commonly seen in foreign exchange rate options is due to the higher probability of a price change of between one and two standard deviations from the mean than would be expected if prices are lognormally distributed.