Lesson 4

Time is a tax

Every day the clock moves, a long option is a little less of a promise and a little more of a leftover.

Hold the stock still in your head. Same price, same vol, one day later. The call is cheaper. The put is cheaper. That drop is theta.

It is not a punishment. It is the market charging you rent for a chance that has one fewer day to happen.

Value of an at-the-money call as days run out, stock unchanged The call starts near $4 and falls toward zero as expiry approaches, steeper in the last two weeks. 42 days expiry 100-call, spot held at $100
Same stock, same vol, fewer days. The premium falls. That drop is the tax.

Two consequences, both practical:

This is why “I will just buy a cheap far out-of-the-money call” is usually a bad sentence. Cheap often means almost no chance left, and the clock is still running.

Check

You own a call. ACME does not move for a week. Vol is unchanged. What happens to the call?