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How do the price of options change as you get closer to earnings, if the stock doesn't change?

Let's say, there's a call option that's worth $6.00 today for a strike price of $62.00 with the stock valued at $60.00 right now.

it usually moves a lot on earnings, and the earnings date is 1 month away.

If the stock remains at $62.00 the day before earnings, will the call option usually be worth more than $6.00, less than $6.00, or the same?

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It all depends on how much uncertainty there is for the stock. With one day to go, a $6 price on a $2 out-of-the-money option seems implausible. It represents an implied volatility of over 500%. It would mean that the option market thinks that there's a decent chance that there is an earnings surprise that shoots the stock up at least $6 (10%) in one day, and that expectation is not present in the actual price of the stock.

The implied volatility (uncertainty) would have to skyrocket for the option price to be the same with one day to go as it was with 30 days to go (all else being equal).

So to answer your multiple-choice question, most likely the option would be worth less than $6.

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An accurate guestimate cannot be made because there are missing variables - expiration date and for reference purposes, how much has implied volatility expanded for previous earnings announcements? (IVolatility offers free 1 year graphs of IV and associated stats).

The time premium of an option decays every day of its existence. If it's a LEAP, it's almost neglible. If it's a standard option, a loose rule of thumb for ATM options is that the theta decay is related to the square root of the time remaining. IOW, it accelerates as time passes.

If your call has 9 months until expiration, there won't be a lot of time decay over the next month.

If your call expires the day after the earnings announcement, it's going to lose the bulk of that $6 by the time the EA occurs a month from now.

Working in opposition is implied volatility which tends to start expanding 4-6 weeks before the EA, inflating option premium and accelerating as the EA nears.

The short answer? If the premium increase due to IV expansion exceeds the time decay in the next month, your call will be worth more than $6. Conversely, If the time decay in the next month exceeds the premium increase due to IV expansion then your call will be worth less than $6.

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