开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

186****8680 · 2023年07月08日

B答案说的是波动率的变化,价格和波动率不是反向的吗

NO.PZ2022071105000016

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.

B答案说的是波动率的变化,价格和波动率不是反向的吗

1 个答案
已采纳答案

李坏_品职助教 · 2023年07月08日

嗨,爱思考的PZer你好:


无论什么期权,都是波动率越大,期权价格(就是期权费)越高。


题目问的是,用隐含波动率的分布(就是波动率微笑那种分布)推算出来的虚值看涨期权价格和外汇期权价格,与对数正态分布相比,是大还是小?


首先,股票期权的波动率微笑指的是:标的股票价格的隐含分布比对数正态分布有更肥的左尾和更薄的右尾,所以虚值看涨期权(行权价格很高,对应右尾)的价格会比正态分布算出来更低廉。


然后,外汇期权的波动率微笑指的是:外汇汇率的隐含分布比对数正态分布有更肥的左尾和右尾,所以虚值外汇看涨期权的价格比对数正态分布算出来的更高。

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

  • 1

    回答
  • 0

    关注
  • 234

    浏览
相关问题