Financial Risk Manager Part 2

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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?

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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.

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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.

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.

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.