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

比夏 · 2021年08月08日

分布的heavier tail是怎么推导到price low or high的?

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.

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.


——关于答案解析的这一段,我的问题在于:如果说volatility smile的分布比lognormal distribution更具有肥尾的特征,那么volatility smiled下对deep-out-of-the-money的定价会更高,是怎么推导出来的?中间还存在哪些逻辑链条?

1 个答案

品职答疑小助手雍 · 2021年08月08日

嗨,从没放弃的小努力你好:


讲义里有那个lognormal对应implied的图的,implied尾巴更肥,也就是对于currency来说出现极端汇率的情况(概率)比lognormal要大,那么更可能产生极端的异常值的话也就是远端波动率会大,那么远端的期权价格也比lognormal假设的要高。这点在这章基础班1.5倍速8分钟的位置李老师讲了的。

----------------------------------------------
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
  • 783

    浏览
相关问题

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. “Using the lognorminsteof the implierisk-neutrprobability stribution will tento”这句话的意思是不是用 lognormal替代之后,价格是比implierisk-neutrprobability stribution的高还是低嘛?equity的Volatility的lognormal的分布比implierisk-neutrprobability stribution的右侧是更肥,价格应该更高;对于currencyVolatility的lognormal的分布比implierisk-neutrprobability stribution的右侧是更瘦,价格应该更低。

2023-08-02 15:16 1 · 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

NO.PZ2018122701000092 Prithe option on Frelatively low anprithe option on EUR/JPY relatively high. 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. 因为FBX是equity,所以在OTM call这边,比lognormal瘦,所以lognormal的价格比implievoliatily的高,那个foregin的是currency,那么OTM call 比lognorm肥,所以lognormal的价格比implievoliatily的低。这么理解对吗

2021-03-19 10:36 1 · 回答