Now, what is then volatility?
Volatility is a measure that gives you an idea on how much the price of an asset, in this case an option, can vary during a specific period of time. The higher the volatility, the higher the chance of the asset moving on a larger range of prices. So for example if a stock is priced at $100, and the volatility is estimated at 20% for that stock, then we can say that there is approximately a 68% chance that the stock will move between $100 - 20% and $100 + 20% during the next 12 months. That is, that there is a chance of around 2 out of 3 times that the stock will move between $80 and $120 next year.
The consequence of that, is that for a volatile asset options will be more expensive, because since they can move on a larger range of prices, there is a higher chance that they will be "in the money" or hit traders' targets over time, both for the up and the down side. This fact makes them intrinsically more attractive and therefore expensive. There is a volatility value associated to each option at different strike prices.
The other thing that can artificially increase the price of options is when there is too much demand of options at a specific strike price. In that case the price of the contracts at that strike price tend to increase. Also when there is too much fear in the markets, traders by more puts, which increases the prices of the puts versus the calls.
The difference between the volatility of different strike price options is known as skew. We can be talking about differences in options that expire the same month, or between options that expire in different months.
Now, as a neutral trader we can take advantage of this pricing issue if we could sell options that are intrinsically more expensive while at the same time protecting our position buy buying cheaper options. Essentially we want to sell the options with higher volatility and buy protection with options of cheaper volatility.
Let's say company ABC is listed at $100. The options chain for November tells you that the 100 Strike price puts are worth 3.50, and the volatility for those is 35%. At the same time the 95 strike puts and the 105 strike puts have a volatility minor than the 100 strike put, and are listed at 1.20 and 6.00 respectively. Well this is a good place for a butterfly, where you sell two 100 strike puts and by protection in the wings by acquiring the 95 and 105 strike puts. The idea is that you are selling the high volatility (more expensive options) while buying the low volatility (cheaper options). Volatility tends to move over time, and in a trade like this one, odds are in your favor that the volatility of the 100 strike put will at some point decrease and be similar to the near strikes volatility, which would yield profit in your position.
Another idea is that if options of a certain month are in general less volatile compared to historical values, strategies such as the Strangle or Straddle could yield good returns should the volatility go up and align itself with the historical average values.
And last but not least, Calendars. Many traders will just trade calendars benefiting from volatility skews. Trying to find the option that is overpriced in the near month with a corresponding under prized sibling in the farther month for protection. When trading calendars always try to have the volatility skew in your favor.
Trading volatility is such a powerful concept that many traders will just trade based on volatility. Volatility is in fact the most powerful component in an option pricing model, the one that moves prices the most. You can buy an undervalued lower volatility option, and the next day it can be worth more money without the price of the stock changing at all. On the other hand, you can have a call option with high volatility, you entered the position ignoring that number and therefore you ended up buying an overpriced option. The next day the stock moves 3 points in your favor but the volatility of the option goes down. Guess what? Your call option may now be worth less money than yesterday!
There are several resources out there about volatility and how to benefit from them. I personally follow this blog where the authors explain trade ideas only based on volatility skews, and they do it openly and for free. I have not played any of his ideas, but the only reading of their articles have taught me a lot in advance.