Why is the price of the option MORE volatile than the price of the underlying stock?

Can you post the question? The only reason that I can think of is that they are looking at % change in option price. For instance, say the option on a $100 stock is worth $5 and has 0.5 delta. If the stock moves $1, the option moves $0.5. So, the change in option price is 10% while the change in stock price is only 1%.
Of course, this is a very naive way of looking at option prices. I can’t think of another explanation though. In general, option prices have delta between 0 and 1.
 
To take it a step further, look at an option that is deep in the money. At that point, deltas are very high and the price of the option will move at almost a 1:1 ratio. So for example if you have a call worth 5$ with an exercise price of $15 and the underlying asset price is $20, a one dollar increase in the underlying (5%) results in a one dollar move in the option to $6 (20%). It isn’t a perfect relationship in practice, but you should be able to understand the logic. If the stock price rises a given amount, you could exercise the option immediately and capture that gain, making it relatively risk free.
 
The question is here:
Which of the following statements about put and call options is least correct?
  1. The price of the option is less volatile than the price of the underlying stock.
  2. Options prices are generally higher the longer the time until the expiration.
  3. For put options, the higher the strike price relative to the stock’s underlying price, the more the put is worth.
I was sure C is correct. I chose B cuz I was a bit messed up with the concept of interest rate volatility. Like a higher discount rate will make the present value of the exercise price lower, so the value of an European Put option (X/(1+RFR)t –S) will be lower….
I didn’t see the delta for option price yet. Is it gonna be covered later in the material or what? I am on Reading 63 now…
 
The 1st choice is senseless. You can’t speculate about the behavior of the option price’s volatility unless you’re aware of the inputs - delta, gamma, time to expiration, etc. Ignorning the 1st choice, your choice is correct.
It’s OK to doubt yourself, but also keep in mind that Schweser is not always right. This is especially true at L2 where their material is littered with inaccuracies.
 
Statements B and C are 90% to 100% correct. Statement A is only 80% correct, in my opinion. I would still choose A based on those choices, but the question is not very good…
 
Delta is just the change in price of underlying relative to the change in price of option, and I don’t think it’s covered in L1 so don’t worry about option greeks for now.
But going back to your question:
A is the correct answer. Option prices are MORE volatile than price of underlying. Look at ohai’s explanation above (ignore the delta part if you don’t understand it, or google options delta)
Statement B is correct. Based on what we learn for L1, option price = intrinsic + time value. The further away you’re from expiration, the higher the time value -> higher option price.
I guess you can also think of it this way: the longer the time you have before expiration, the higher the chance that the stock can go in the money, so it will cost you more to buy that option; thus the higher option price. You’re making the problem way too complicated by going into interest rate volatility.
Statement C is correct (you already got this)
Since question is asking for statement that’s least correct, the answer is A :) I hope my explanation makes sense lol.
 
A very obvious difference is that options have time value of money that stocks don’t
 
iteracom wrote:A very obvious difference is that options have time value of money that stocks don’t
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That was my first thought. What does the Schweser explanation say?
 
I think the most suitable understanding would be the existence of leverage in the option.
 
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