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You kind of answered the question yourself. Precisely because different market participants use different inputs to their pricing models, it is much easier to quote one single input (implied vols) than the output of 5 different inputs (BS option price). What is important is that you clearly differentiate between quoting and agreeing on the trade vs. the ...

This is an example of minimum price variation (also known as the minimum price increment or the minimum price fluctuation). All public quotes for US equities are displayed to the nearest penny. (Hidden quotes may be entered at sub-penny increments.) US stock indices follow this convention and thus quote to the nearest penny. The oil listing is odd indeed. ...