As days tick off of call options, time value decays. My question is does that happen automatically at 9:30AM at market open or does it get continuously deducted as the day ticks on?
The time value decay is theoretically constant. In reality, it is driven by supply and demand, just like everything else in the market.
For instance, if a big earnings announcement is coming out after the close for the day, you may see little or no time decay in the price of the options during the day before.
Also, while in theory options have a set value as related to the trading price of the underlying security, that does not mean there will always be a buyer willing to pay a premium as they come close to expiration (in the last few minutes). You can't forget to account for the transaction fees associated with buying the options, or the risk factor involved.
It is rare, but there are times I've actually had to sell in the money calls at a penny or two LESS than they're actually worth at the time just to unload them in the last few minutes before the market closed on expiration day.
If you're talking about just Theta, the amount of decay due to the passage of time (all else being equal), then theoretically, the time value is a continuous function, so it would decay throughout the day (although by the day of expiry the time value is very, very small). Which makes sense, since even with 15 minutes to go, there's still a 50/50 shot of an ATM option expiring in-the-money, so there should be some time value associated with that one-sided probability. The further away from ATM the option is, the smaller the time value will be, and will be virtually zero for options that are deep in- or out-of-the-money.
If you're talking about total time value, then yes it will definitely change during the day, since the underlying components (volatility, underlying price, etc.) change more or less continuously.
The time value of the option (theta) decays constantly (by the millisecond)
As it is one of the inputs to the option pricing model, it usually has a lower impact on the overall option price than other changes in the market.
As the (US) markets price options in penny ($0.01) or nickel ($0.05) increments, you will only observe these changes when the impact of theta is big enough for the market maker to increase or decrease his bid or offer by another $0.01 or $0.05.
This will happen slowly throughout the day but should be more significant from one day’s close to the next day’s open particularly if there is a weekend or long weekend in between.