option price volatility

Question 3 from reading 73 Schweser. Why are option prices more volatile than the underlying stock? An option’s price will increase with an increase in volatility, but won’t it stay fairly constant for a fixed volatility?

If you consider the black scholes model, there are five inputs to the the price. I.e. even if the volatility stays roughly the same, there are other forces at work. Time is probably the most relevant. For example, imagine you had an 6 month option, and the volatility stayed the same for two months. The value would still change mainly due to the theta loss. Or consider rates, if they increased the value would change, but the volatility could stay the same. At least, that’s my understanding. (I haven’t finished all the readings yet!! :slight_smile:

You should have a look at the delta

Isura Wrote: ------------------------------------------------------- > Question 3 from reading 73 Schweser. > > Why are option prices more volatile than the > underlying stock? An option’s price will increase > with an increase in volatility, but won’t it stay > fairly constant for a fixed volatility? I think it’s a bad question. A way out of the money option will not be too volatile regardless of what the underlying does.