I have sometimes witnessed the price of deep in-the-money option contracts of the same underlying, but different expiration dates, go in different directions by the end of the trading day. This makes no sense to me.
The intrinsic value of both options should be directly correlated to the price of the underlying. For example, in case of put options, if the underlying's price goes up, the intrinsic value of both options should go down in equal amounts.
The extrinsic value should behave similarly. Each day that passes, both options experience time decay, so both option's extrinsic value should go down accordingly (though not necessarily by equal amounts). If the underlying's implied volatility changes, the extrinsic values of both options should move in the same direction as well.
So, how is it possible that one option could end up on any given day with a higher price than the day before, while the other option ends up with a lower price than the day before?