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In this link on SPY options

the Chg column mostly shows 0.00. Does this mean option prices don't change much minute to minute unlike the underlying?

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Notice that a lot of the prices are well off market for options that will close Friday. Most of the action is happening closer to the current market price. The market is roughly $187 now. Almost all the call options with price movement are between $180 and $191. All of the put options with price movement are between $172.50 and $192.

Others have pretty low volume, which may account for no listed price change. A huge number of the listed puts and calls have ask prices of 0.01 because they're going to be worthless on Friday barring a major price change on the underlying instrument.

Small fluctuations in the underlying do not tell you too much about the expected price in a month or two, so there's less reason to buy and trade. However, the bid/ask values of the options will fluctuate with the underlying, even if no trades take place.

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Options are generally much less liquid than the underlying. In particular there are much fewer trades. The "Chg" column is the change with respect to the price at which the last trade has taken place. For many series (in particular options that are far in or out the money) there may be a long time between trades, hence the Chg would be at zero for many days.

The quoted bid and asks generally move with the underlying, otherwise this would open the door to arbitrage possibilities, which would quickly be taken advantage of.

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