B答案说的是波动率的变化，价格和波动率不是反向的吗

问题如下：

A risk committee of the board of company ABC is discussing the difference between pricing deep out-of-the

money call options on ABC stock and pricing deep out-of-the-money call options on the USD/GBP foreign

exchange (FX) rate using the Black-Scholes-Merton model. The committee considers pricing each of these two

options based on two distinct probability distributions of underlying asset prices at the option expiration date:

a lognormal probability distribution, and an implied risk-neutral probability distribution obtained from the

volatility smile for each aforementioned option of the same maturity and the same moneyness. If the implied

risk-neutral probability distribution is used instead of the lognormal distribution, which of the following is

correct?

选项：

A.

The price of the option on ABC stock would be relatively high and the price of the option on USD/GBP FX

rate would be relatively low compared to those computed from the lognormal counterparts.

B.

The price of the option on ABC stock would be relatively low and the price of the option on USD/GBP FX

rate would be relatively high compared to those computed from the lognormal counterparts.

C.

The price of the option on ABC stock would be relatively low and the price of the option on USD/GBP FX

rate would be relatively low compared to those computed from the lognormal counterparts.

D.

The price of the option on ABC stock would be relatively high and the price of the option on USD/GBP FX

rate would be relatively high compared to those computed from the lognormal counterparts.

解释：

中文解析：

B是正确的。用波动率微笑推导出来的标的股票价格的隐含分布与对数正态相比，有更肥的左尾和更薄的右尾。因此，使用隐含的价格分布计算出来的高度虚值看涨期权，其价格会比对数正态分布算出来的结果更低。

用波动率微笑推导出来的标的外汇的隐含分布，比对数正态分布有更肥的左右尾。因此，使用隐含分布计算出来的高度虚值看涨期权的价格会比对数正态分布算出来的价格更高。

B is correct. The implied distribution of the underlying equity prices derived using the

general volatility smile of equity options has a heavier left tail and a less heavy right tail

than a lognormal distribution of underlying prices. Therefore, using the implied

distribution of prices causes deep-out-of-the-money call options on the underlying to be

priced relatively low compared with using the lognormal distribution.

The implied distribution of underlying foreign currency prices derived using the general

volatility smile of foreign currency options has heavier tails than a lognormal distribution

of underlying prices.

Therefore, using the implied distribution of prices causes deep-out-of-the-money call

options on the underlying to be priced relatively high compared with using the lognormal

distribution.