This makes no sense. Simply exercising an option is not a taxable event--you're just trading a contract for shares of a stock. There's no money going into your bank account.
Furthermore, you aren't taxed short-term capital gains when you haven't realized a profit. You'd need to exercise AND sell at $100 / share for those gains to be taxable. The correct taxable amount in this scenario would be $9 / share ($1 spent, $10 earned, net gains = $9).
[1] Assuming you meant "exercise at $100" here.