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Amy · 2023年08月02日

梳理一下思路

NO.PZ2018122701000092

问题如下:

A committee of risk management practitioner discusses the difference between pricing deep out-of-the-money call options on FBX stock and pricing deep out-of-the-money call options on the EUR/JPY foreign exchange rate using the Black-Scholes-Merton (BSM) model. The practitioners price these options based on two distinct probability distributions of underlying asset prices at the option expiration date:

  • A lognormal probability distribution
  • An implied risk-neutral probability distribution obtained from the volatility smile for options of the same maturity

Using the lognormal instead of the implied risk-neutral probability distribution will tend to:

选项:

A.

Price the option on FBX relatively high and price the option on EUR/JPY relatively low.

B.

Price the option on FBX relatively low and price the option on EUR/JPY relatively high.

C.

Price the option on FBX relatively low and price the option on EUR/JPY relatively low.

D.

Price the option on FBX relatively high and price the option on EUR/JPY relatively high.

解释:

A is correct.

考点 Volatility Smile

解析

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 lognormal distribution of prices causes deep-out-of-the-money call options on the underlying to be priced relatively high.

The implied distribution of underling foreign currency prices derived using the general volatility smile of foreign currency options has heavier tail than a lognormal distribution of underlying prices. Therefore, using the lognormal distribution of prices causes deep-out-of-the-money call options on the underlying to be priced relatively low.

“Using the lognormal instead of the implied risk-neutral probability distribution will tend to”这句话的意思是不是用 lognormal替代之后,价格是比implied risk-neutral probability distribution的高还是低嘛?equity的Volatility的lognormal的分布比implied risk-neutral probability distribution的右侧是更肥,价格应该更高;对于currencyVolatility的lognormal的分布比implied risk-neutral probability distribution的右侧是更瘦,价格应该更低。

1 个答案
已采纳答案

pzqa27 · 2023年08月03日

嗨,爱思考的PZer你好:


是的当使用对数正态分布替代从波动率微笑中得到的隐含风险中性概率分布时,将会导致以下情况:

  1. 对于FBX股票,深度虚值看涨期权(deep out-of-the-money call options)的价格会相对较高。
  2. 对于EUR/JPY外汇汇率,深度虚值看涨期权的价格会相对较低。


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NO.PZ2018122701000092问题如下 A committee of risk management practitioner scusses the fferenbetween pricing ep out-of-the-money call options on Fstoanpricing ep out-of-the-money call options on the EUR/JPY foreign exchange rate using the Black-Scholes-Merton (BSM) mol. The practitioners prithese options baseon two stinprobability stributions of unrlying asset prices the option expiration te: A lognormprobability stribution implierisk-neutrprobability stribution obtainefrom the volatility smile for options of the same maturityUsing the lognorminsteof the implierisk-neutrprobability stribution will tento: A.Prithe option on Frelatively high anprithe option on EUR/JPY relatively low.B.Prithe option on Frelatively low anprithe option on EUR/JPY relatively high.C.Prithe option on Frelatively low anprithe option on EUR/JPY relatively low. Prithe option on Frelatively high anprithe option on EUR/JPY relatively high. A is correct.考点 Volatility Smile解析 The impliestribution of the unrlying equity prices riveusing the genervolatility smile of equity options ha heavier left tail ana less heavy right tail tha lognormstribution of unrlying prices. Therefore, using the lognormstribution of prices causes ep-out-of-the-money call options on the unrlying to pricerelatively high.The impliestribution of unrling foreign currenprices riveusing the genervolatility smile of foreign currenoptions hheavier tail tha lognormstribution of unrlying prices. Therefore, using the lognormstribution of prices causes ep-out-of-the-money call options on the unrlying to pricerelatively low. 题目不知道什么意思?很多条件都干啥用?答案都分别是什么意思?

2023-08-08 18:28 3 · 回答

NO.PZ2018122701000092 问题如下 A committee of risk management practitioner scusses the fferenbetween pricing ep out-of-the-money call options on Fstoanpricing ep out-of-the-money call options on the EUR/JPY foreign exchange rate using the Black-Scholes-Merton (BSM) mol. The practitioners prithese options baseon two stinprobability stributions of unrlying asset prices the option expiration te: A lognormprobability stribution implierisk-neutrprobability stribution obtainefrom the volatility smile for options of the same maturityUsing the lognorminsteof the implierisk-neutrprobability stribution will tento: A.Prithe option on Frelatively high anprithe option on EUR/JPY relatively low. B.Prithe option on Frelatively low anprithe option on EUR/JPY relatively high. C.Prithe option on Frelatively low anprithe option on EUR/JPY relatively low. Prithe option on Frelatively high anprithe option on EUR/JPY relatively high. A is correct.考点 Volatility Smile解析 The impliestribution of the unrlying equity prices riveusing the genervolatility smile of equity options ha heavier left tail ana less heavy right tail tha lognormstribution of unrlying prices. Therefore, using the lognormstribution of prices causes ep-out-of-the-money call options on the unrlying to pricerelatively high.The impliestribution of unrling foreign currenprices riveusing the genervolatility smile of foreign currenoptions hheavier tail tha lognormstribution of unrlying prices. Therefore, using the lognormstribution of prices causes ep-out-of-the-money call options on the unrlying to pricerelatively low. 这道题还是不懂诶,可否麻烦老师用中文讲解一下哦~

2022-10-02 13:46 1 · 回答

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2021-08-08 10:37 1 · 回答

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2021-03-19 10:36 1 · 回答