So, as a California resident, my accountants advised various stuff. This is advice from them to me, obviously I'm not qualified to give this advice to anyone else, and anyway I don't know others' situations, so don't blame me.
I don't currently have to pay estimated tax. I believe their answers would be different if I did. I almost certainly will have to next year.
In December I should figure out how much capital gains (long term and short term) I made on all my trading this calendar year. This will actually be easy for me, since I keep a spreadsheet with all the trades. I could probably also get the same info from my broker, but I maintain the spreadsheet so that I'm continually reviewing the consequences of my good and bad trades.
Then, in December, I should pre-pay the CA state tax I estimate. This is because it's deductible from the income for Federal tax in the year in which it is
paid, not the year it's due, so this will even out the total amount at least a little bit. Note that if you need to pay more than a certain amount (I forget how much, but if you're thinking about the problem, this means you!) CA now insists that it must be paid electronically, and it takes a non-trivial amount of time to set up to do that, so don't leave it till the last minute.
I can wait until April to pay the Federal tax. Note that this will probably require not only the actual estimated tax (my tax always takes longer to finalize, due to being Australian and having investments over there, but you have to pay up front), but I will probably have to pay quarterly estimated tax for the 2014 following year.
They also put in a very strong hint to make sure that I have enough money on hand to pay what I need to pay. This is important advice. If it's all tied up in Tesla stock, and everyone needs to cash out at the same time, it could easily force the price down. If you need proof, look back to 2001, and note just when the real dip from the Internet Bubble hit; it was pretty close to when all the Sillycon Valley people's tax came due on all the bubble stocks from 2000. While I personally avoided that trap, I have a friend who lost his house over it; he owed more tax on the profits from 2000 than the investments were worth in April 2001.
As AudobonB said, if you keep holding you don't owe the tax yet! Wait until you retire then sell it in little bits
Of course you can't hold options that way; they expire! If you sell the options before expiry for a profit, that is (probably short term) capital gains. But if they were calls, and you exercise them and turn them into shares, you just add the cost of the calls to the cost basis of the converted shares, and don't owe any tax yet. However the clock restarts for the holding period, so you have to wait a year from exercise before the gains become long term, no matter how long you held the options.