NO.PZ2023100703000124
问题如下：
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?选项：
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.
解释：
C is correct. Demand for protective puts will increase the price of these puts, which will increase their implied volatilities, which creates a downward sloping volatility skew. A is incorrect. The volatility smile commonly seen in equity options is downward sloping with higher implied volatility in lower strike prices and lower implied volatility in higher strike prices. This implies a greater probability of seeing a price in the left hand tail and a lower probability of seeing a price in the right hand tail than in the lognormal distribution. B is incorrect. The volatility smile commonly seen in foreign exchange rate options implies a greater probability of the future rate being either <1 standard deviation or >2 standard deviations away from the mean, and a lower probability of the future rate being between 1 and 2 standard deviations away from the mean. D is incorrect. Since the central bank announcements are unexpected the volatility curve will not be shaped with higher implied volatilities at-the-money than out-of-the-money. Protection will most likely be bought using out-of-the-money options which will create a volatility smile, rather than a frown.B为什么在1-2倍标准差和1倍内2倍外的结论是不一样的，可以从那个微笑曲线图看出来吗 D没看懂，是volatility frown的话看起来结论没问题？
