This is a question about why options prices do not take volume into account. The popular option valuation formula "black-scholes" certainly does not account for this and I don't suggest that it does.
But one could hold a large option position while the underlying asset's price walks up or down on very low volume, allowing the option to gain more and more value and be liquidated without affecting the market for the underlying asset. This seems strange to me, since it would seem to me that the option's value/price should have a liquidity premium for exercising the option and closing the position on the underlying asset, despite the fact that most options are not exercised.
I like the inefficiencies in option pricing, as a speculative tool and the predictability in calculating intrinsic value as an in the money option moves deeper in the money. But it seems that volume weighted price nearer expiration should determine the price of an option's intrinsic value in the black-scholes formula
Thoughts and insight appreciated