This is not correct. Stock options can decrease volatility and serve as insurance against large increases or decreases. That is the point of hedging.
For example if I have 100 shares of AAPL @108 and I'm nervous of it dropping below $80 in the near future, I may buy a MAR16 put option at $90/share for a few pennies in the hopes that if the stock does actually decrease to a level that makes me feel uncomfortable, the options will increase enough to offset the stock loses.
So they very much can be insurance. It just depends on how you play them.
Your comment makes sense if you're talking about using publicly-traded derivatives to hedge long or short positions in a diversified portfolio.
The comment to which you replied was talking about employee stock options, which are not generally used to hedge a short position, and often represent a large part of someone's overall wealth and/or income.
Sorry, I was unclear. As a sibling pointed out, the question at hand is private employee stock option grants, which act as a lottery ticket because they are usually worth nothing but sometimes worth a very large amount if the company goes public or gets bought.
You are of course correct that stock options on the public market are most often used to hedge and thus they do act like insurance. It seems fairly certain that this is not what OP had in mind, though.
For example if I have 100 shares of AAPL @108 and I'm nervous of it dropping below $80 in the near future, I may buy a MAR16 put option at $90/share for a few pennies in the hopes that if the stock does actually decrease to a level that makes me feel uncomfortable, the options will increase enough to offset the stock loses.
So they very much can be insurance. It just depends on how you play them.