关于sticky strike和sticky moneyness

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

请问一下期权的基础资产价格变化对Implied Volatility变化的影响中有题述的两种影响。烦请大神用通俗的语言解释一下这两种影响分别是什么？两种影响有什么关系？是为了分析需要，而把一个整体的变化分成了两种变化呢，还是本来就是两个互相独立的影响？

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏2 回帖

关键词：Sticky Strike Stick money Tick 价格变化 影响

It is just two different views of the people in the market.

when the underlying stock's price changes,

some people believe the skewness of the volatility will be stick to the strike

while

other people believe the skewness will be stick to the moneyness

for example, there are three strikes 10, 20, 30, and the stock price is currently  20

if the stock price goes from 20 to 30. for sticky strike hypothesis, the skewness of the volatility will not move with respect to the strike. But for the sticky moneyness hypothesis, it will move. Since the at the money option is now 30 not 20, the lowest point of the volatility smile for example will move from 20 to 30. And of course, 20 is now in or out of money not at the money.

Both the sticky strike and sticky moneyness rules have been proven to provide arbitrage oppportunities. However, these rules do help us understand the risks of the volatility smiles.

best,

Chemist_MZ 发表于 2014-1-20 23:30
It is just two different views of the people in the market.

when the underlying stock's price cha ...

非常感谢！
不过还有两个问题：
1.为什么at the money是最低点，直观的解释或现实的表现是什么？
2.sticky strike是说基础资产的价格变化对volatility skewness没有任何影响吗？如果是的话,那这个假说有啥实际意义呢？
谢谢了！

1. Think it this way, if there is no smile and the vol is flat. the marginal distribution is strickly lognormal.

However in reality, protection buyer (out of the money put buyer) see it as more right hand side skewed while out of the money call buyer sees it as more left hand skewed. these skews at both sides impied a fatter tail distribution than lognormal therefore larger implied vol at both ends

One fact to point out is that, at the money point is not strickly the lowest point. It is near it but not exactly the same

2. this assumption is simply to address how the volatility will evolve along with underlying spot.

From a market prospective, people use sticky strike convention for equity cos people trade on strike for listed options while in FX world people use sticky delta convention cause people trade on delta (spot change too fast)

as from modelling prospective, in general sticky strike model works well for short term but the sticky delta model is better for longer term. For detail you could refer to paper by Derman which explains it ina very intuitive fasion

wjve 发表于 2014-1-21 08:15
非常感谢！
不过还有两个问题：
1.为什么at the money是最低点，直观的解释或现实的表现是什么？

1. Since the empirical distribution of the stock price has a so-called fat tail phenomena which means the stock price will go to the two tails much often than the log-normal distribution indicates (BS model). So the volatility implied by deep in the money and out of money option will be larger than that of BS model. That's why at the money option will be the lowest.

2. This assumption is very bad actually. You know people in the industry focus on the usefulness not reasonableness.

best,

Chemist_MZ 发表于 2014-1-21 10:51
1. Since the empirical distribution of the stock price has a so-called fat tail phenomena which me ...

哦？为什么实际的价格分布是fat tail，就能说明atm时的volatility最小呢？

wjve 发表于 2014-1-21 13:56
哦？为什么实际的价格分布是fat tail，就能说明atm时的volatility最小呢？

This is only an approximate result not guaranteed. e.g. can be a volatility skew. And I said ATM is the lowest just for simplicity. The lowest point should be around ATM.

The reason I have explained, if no fat tail: the volatility for say three strikes in the money at the money out of money are say 0.2,0.2,0.2, if fat tail it will be 0.3, 0.2, 0.35. ATM volatility will not necessarily stay the same. Just an example

the logic for fat tail's affection is as follows:

1. In reality, the stock distribution is fat tail (fatter than lognormal)

2. This means that the stock will go very high or very low with a higher probability compared with lognormal.

3. In this case, of course, the lognormal BS model underprice the option that is deep OTM call and put (PS: 1. since ITM, especilaly deep ITM is less sensitive to volatility we ignore the affection. 2. The affection should be analyzed case by case. It can have volatility skew. Here, I assume it is a smile)

4. But you still should use log normal and BS formula right? the only thing you can do is increase the implied volatility.

5. The implied volatility on the two ends increases and, of course, the volatility in the middle will be lower comparatively.

This is the main draw back of the BS model. It is not self-consistant. If there is a volatility smile, actually the stock price is not lognormal.

hope it's clear now.

best,

stoneyl 发表于 2014-1-21 10:38
1. Think it this way, if there is no smile and the vol is flat. the marginal distribution is strickl ...

谢谢，请问为啥不存在smile，volatility图形是平的时候，marginal distribution就是lognormal的？这个marginal distribution是基础资产的年收益率吗？

wjve 发表于 2014-1-21 14:33
谢谢，请问为啥不存在smile，volatility图形是平的时候，marginal distribution就是lognormal的？这个mar ...

Remember you are using the BS model.

"Implied volatility" ONLY refers to the volatility implied by BS model. Since BS model assumes the lognormal underlying price with CONSTANT volatility. Of course if the implied volatility is constant (flat) across all strikes, the distribution is certainly lognormal.

wjve 发表于 2014-1-21 14:33
谢谢，请问为啥不存在smile，volatility图形是平的时候，marginal distribution就是lognormal的？这个mar ...

Lognormal is the distribution of the stock price, NOT return.

The log return of the Stock is Normal.

All the units in the model is in year.