Nice question.

These are just common phenomenon but not rules

For OTM option, people usually bet that they will be ITM or ATM in the future. You know, when option move from OTM to ITM or ATM, its value increases sharply, which will bring much profit. And, for another reason, OTM are usually very cheap. The bet cost is relatively very low.

So for these two reasons, people tend to love OTM option for speculation. So generally, these options are traded more often so they fluctuate more than ITM option comparatively.

Considering time to maturity. If an option is very close to expiration, because there are less uncertainty of the stock price compared with longer time to maturity, the options time value drops sharply. And, on the other hand, because the future is much more clear in the short term, people tend to know the option in their hands has how much value approximately. So if the option is overpriced, people will sell it to avoid the loss, if it is underpriced, people will buy it. So they fluctuate more. (Just imaging that an option will expire tomorrow, and an option will expire in a year. You have a much more clear idea on the former one)

I don't think there is a definite answer to the last question. Basically, the OTM options will be worthless and don't fluctuate if the time to maturity is very short, since the future is very clear. Imagine that you hold a IBM stock call option with a strike of 200, and it will expire tomorrow. The IBM stock price today is 100, then, this option will have approximately 0 trade volume. If the market is efficient, this option should have a price of zero. However, there will be some misplacing, like, the option is still traded at 10 bucks. Then people tend to short it to make money. So the price will drop very sharply from 10 to 0 which is large fluctuation. However, if there is no mispricing, I don't think the fluctuation of short term OTM option will dominate the long term ITM option. Unless there is a mispricing.

For summary, I want to remind you that, when you consider these kinds of questions, you should put the time value of the option in the first place. No matter the option is ITM ATM or OTM, they have a common feature——volatility of their underlying stock. If there is more uncertainty, they will have more value, and people are willing to bet. And if they are mispriced which means the uncertainty does not make the option have such much value, people will take advantage of such mispricing. Both these two situations will make the option fluctuate a lot.

Last thing is that, always remember, when you trade option, you actually trade uncertainty, or the risk, or specifically, the volatility.
Hope help~

你太牛了。谢谢
还有我之前interview的时候被问到一条问题：
Just one day before the expiration.  Would you hedge gamma or vega for you long call position ?
我应该什么回应？
I will hedge the gamma for this long call position because gamma will fluctuate enormously just right before the expiration, where gamma is the acceleration of Delta and Delta is the rate of change of the options value with respect to the underlying price.  Hence, in order to hedge the risk the the long option position we should hedge gamma.
不知道我答的对不对哦。。。

嘿嘿，不敢~

同胞之间还是说中文吧~我会分情况讨论，其实call到期的前一天，已经差不多是一根折线了，因此除了在strike price 的地方，其他地方的convexity都是0（我们知道只有曲线才有凸性，而直线没有，而凸性又是用二阶倒数衡量的，即Gamma），既然没有gamma风险，所以我觉得只要不是ATM，我就只要delta hedge就行了。如果股价在ATM附近，gamma会很大，理论上说是无穷，因为delta会瞬间从0，跳到1，所以我会hedge，这时候应该是期权对gamma最敏感的时候。

对于vega，他的形态、形状和gamma差不多，近似地说，如果你hedge的时候把portfolio弄成gamma neutral了，他一般自然就近似称为为vega neutral了。

所以总结一下，只有在ATM附近我才会hedge gamma和vega，否则就不hedge。