Why are stock options more volatile than the parent stock?

Can you answer in simple english please? I really want to understand this.Why are stock options more volatile than the parent stock?
Options are more volatile because they cost less.





For example, is a stock is selling for $25 per share a short term call option with a $25 strike might trade at $0.50 per share. If the stock goes up to $26.00 per share, that option might increase in price to $1.25 per share.





Even though the stock price changed $1.00 and the option price only changed $0.75, the option price changes a much higher percentage of its value.





A $1.00 increase for a $25 stock = a 4% increase.


A $0.75 increase for a $0.50 option = a 150% increase.Why are stock options more volatile than the parent stock?
Because they are valid for a limited period of time only and because the price of an option is only a fraction of the price of the underlying (not parent) stock, even though the option will tend to rise or fall (more or less) as many dollars as the price variation in the underlying shares.
With an option, your are not buying the stock, you are instead buying the ability to buy a stock at a certain price in the future. So you are betting on the difference between todays price and a future price, without actually buying the stock today. Here is an example:





A stock is selling for $100 a share today. You think in 90 days the stock will be worth $110, but the market only thinks it will be worth $105. The market will sell you an option to buy the stock 90 days from now at today's price ($100), but they will charge you $5 for that option, because they think the stock will be worth $5 more 90 days from now than it is worth today.





Since you think the stock will instead be worth $10 more, you take that bet and buy the option. You hope that 90 days from now you can exercise that option, which means you will buy the stock for the $100 allowed by the option, and immediately sell it for the $110 you think it will be worth. You would make a profit of $5 ($110 sell price, minus the $100 buy price, minus the $5 you paid for the option).





That is a 100% profit on your $5 option purchase!





If instead you bought the stock, rather than the option, you would have paid $100 for the stock, and sold it for $110, which would only be a 10% profit.





However, the option is much more risky; if you bet wrong, and the stock is only selling for $105 after 90 days, you make no profit at all, and if it is selling for jusy $100, you lose everything you invested. Whereas, if you bought the stock instead of the option, you would still have a stock worth $100. You didn't gain anything, but you didn't lose anything.