It depends on the share price (p say), strike price (k say) and expiry date. Very close to expiry date, the intrinsic value of an option is p-k. So, if p is a long way below k, even a big % rise in p makes no difference (the intrinsic value is still zero). A long way from expiry date, there could be a bit of movement. Most movement occurs when p-k is close to or greater than zero, but movement in option price would still normally be no more than the movement in share price in $ terms. Of course it could be much higher in % terms. Hope that helps. I never buy options, because in the days that I did, they always expired before the share price went up. I eventually worked out that it was usually too easy for the option sellers to hold the share price down until the expiry date. Or maybe I imagined it ...
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