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Answer: Demand for option protection against steep drops in equity prices leads to higher prices in out-of-the-money puts relative to out-of-the-money calls, which creates a downward-sloping implied volatility skew in these options.
## Explanation **C is correct** because: - In equity markets, investors often seek protection against market downturns by purchasing out-of-the-money put options - This increased demand drives up the prices of these puts, which in turn increases their implied volatilities - The result is a downward-sloping volatility skew (not a symmetric smile), where lower strike prices have higher implied volatilities than higher strike prices **A is incorrect** because: - The volatility pattern in equity options is typically a skew (downward sloping) rather than a symmetric smile - The skew implies higher probabilities in the left tail (large price drops) and lower probabilities in the right tail than the lognormal distribution would suggest **B is incorrect** because: - The FX volatility smile suggests higher probabilities for both extreme outcomes (far out-of-the-money puts and calls) - This creates a U-shaped pattern with higher implied volatilities for both low and high strike options - The distribution has fatter tails than the lognormal distribution **D is incorrect** because: - Unexpected central bank announcements would likely lead to increased demand for out-of-the-money options for protection - This would create a volatility smile pattern, not higher implied volatilities specifically for at-the-money options - The protection is typically sought using out-of-the-money options rather than at-the-money options
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An option pricing analyst at an investment bank 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.
C
Demand for option protection against steep drops in equity prices leads to higher prices in out-of-the-money puts relative to out-of-the-money calls, which creates a downward-sloping implied volatility skew in these options.
D
Demand for option protection against the impact of unexpected central bank announcements on foreign exchange rates leads to higher prices, and higher implied volatilities, for at-the-money options relative to out-of-the-money options.