Theta

An option loses value every day the stock does nothing. Nobody has to trade for it to happen; the calendar does it. Theta measures that loss, and it is the price you pay for the gamma you learned about in the last lesson. The two are joined at the hip, and understanding why is most of what this lesson is for.

Time decay per day

Theta is the change in an option's price for one day passing, with the stock and its implied volatility unchanged. The chain quotes it per day, per share, and it is negative for the owner. Say a TSLA call trades at $12.00 with a theta of minus 0.18. Tomorrow, other things equal, it is worth about $11.82. On one contract that is $18 a day walking out the door. Whoever sold the call collects the same $18.

The chain shows the same theta on the call side and the put side at each strike. That is how the data is published: the vendor quotes Greeks on the forward price, and on that basis a call and a put at the same strike share one theta, just as they share one gamma and one vega. Textbook Black-Scholes, which works from the spot price and charges interest on it, splits them slightly: the call loses a little more each day than the put, and the gap is one day's interest on the strike, about 2 cents a day on a $200 strike at a 4% rate. For reading decay off the chain, the one number per strike is the one to use.

Largest at the money

Only time value decays, because intrinsic value is what the option is worth right now and time has nothing to do with it. Time value is largest at the money, where the outcome is least certain, and it all has to reach zero by expiration. So the at-the-money option has the most to lose and the biggest theta. A deep in-the-money option is nearly all intrinsic value and decays slowly. A far out-of-the-money option has very little time value left to lose, so its theta is small too.

Decay accelerates into expiration

An at-the-money option's time value grows roughly with the square root of the time left, not with time itself. Put numbers on it. With 36 days left, an option might carry $6 of time value. With 9 days left, a quarter of the time, it carries about half as much: $3. So the first 27 days cost $3, about 11 cents a day, and the last 9 days cost the other $3, about 33 cents a day. The daily loss triples as expiration gets close. Owning at-the-money options into the last week is expensive, and selling them is where most of the decay is collected.

Theta is the rent you pay for gamma

Look back at the gamma lesson and the pattern is the same: gamma is largest at the money and grows into expiration. That is no coincidence. An option with lots of gamma makes money when the stock moves, and the market charges for that chance every day the stock sits still. Long gamma means paying theta. Short gamma means collecting theta and wearing the risk of a large move. Every option position sits somewhere on that trade-off. The question a trader asks is whether the stock will move enough to earn back the rent, and Module 6 answers it: a hedged option earns its rent back only when the stock moves more than its implied volatility priced.

Your turn

Open the TSLA chain. Read the at-the-money theta on the monthly expiration, then switch to the nearest expiration and read it again. The second number should be noticeably larger in size. Then add the call and put thetas together to get the daily cost of an at-the-money straddle.