You'll need $10K to buy the options from your company. That's "Day 1". By Day 30 you need to file 83b with the IRS. And when it's time to pay your taxes for that year, you'll need to pay the IRS the taxes on the "income" you got from exercising the options. That is, if the strike price is $1 and the current market price for the shares is $3, the IRS sees that as a $20K income you made (even though you don't actually have liquid money).
If the delta between the strike price and the market price is large enough, you might actually pay the IRS more than you'll pay your company.
My understanding is that Day 0 is the only important day here (or actually, Day 365 doesn't matter). You pay $10K on Day 0 and you earn no "income", so you do not owe any tax.
On Day 900, if your shares are worthless, you can then take that $10K as a long-term capital loss. If and how that can carry forward is something you'll want a tax accountant for.
If the delta between the strike price and the market price is large enough, you might actually pay the IRS more than you'll pay your company.