In my notes I have: If Theta is NEGATIVE then the value of the of the call and put option go to 0. In the CFA Sample exam it says :Theta refers to the rate at which the time value decays on an option. Therefore when theta is POSITIVE, as the time to maturity decreases, the price of both a call and a put option will INCREASE" Can someone explain this as I see that this is contradictory. also how can THETA be NEGATIVE?
Theta would be negative if an option is out of the money, if there is a year left, the option would still hold value as volatility and market movements could possibly bring it back into the money. However, if as time decreases no changes take place, the value of the option will decrease as the time window closes in which a price movement in the underlying could occur. Thus increasing the probability that the option will expire out of the money, and worthless.
Theta shows us how much “time value” of an option will erode as time passes (i.e. each trading day). My understanding is as follows and feel free to correct me if I’m wrong… If an option is valued at $5.00 today and has a Theta of -0.30. Assuming no changes in the price of the underying security, the option will decrease in value the next trading day to $4.70 ($5.00 - $0.30). This is simply time value decay. Generally, Theta will be negative with the exception to the rule being that a positive Theta may arise if an option is deep in the money and close to maturity.
I agree with what bhill020 wrote. Usually we think of the time value as being positive. When we do this we are saying since there is time left the option still has a chance to be in the money. Theta is looking from Time=0. So as you move further from 0 your time is decaying and your option will be worth less.
Isn’t that basically what I wrote?
Yeah. But when I ask question I like to get more than one person explaining things because sometimes it clicks better with one person vs another.
Just wanted to make sure I wasn’t going crazy or missing a key detail for my own understanding.
Black Swan, I think you were spot on. Was just trying to use an example, as I know I have an easier time grasping things with examples.
Black Swan Wrote: ------------------------------------------------------- > Just wanted to make sure I wasn’t going crazy or > missing a key detail for my own understanding. I think we all are getting a little crazy at this point. 
Dude, I’m telling you, I’m definitely very insane, I am way too obsessed with CFA, I’ve been going non-stop since October at this pace (LI, CMA while waiting for results, LII) and I definitely need to reconnect with society soon. But you know what makes me absolutely break out a wicked smile from ear to ear? Tomorrow will be our last Saturday spent q-banking, AFing, or even studying CFA materials. I plan on not returning to starbucks after DDay until they change their damn playlist as well, the repitition has definitely fed the crazy level.
mvwt9 can you explain this part you said: “Theta is looking from Time=0. So as you move further from 0 your time is decaying and your option will be worth less.” I get everything else but this.
He means time zero as in T(0)=====>T(1), not the other way around, which I think is the way you’re picturing it.
Wow, I need to have people draw more pictures because seeing the arrow made all the sense in the world.
Niblita75 Wrote: ------------------------------------------------------- > mvwt9 can you explain this part you said: > > “Theta is looking from Time=0. So as you move > further from 0 your time is decaying and your > option will be worth less.” > > I get everything else but this. It isn’t in the books…it is just the way I think about it. I was used to thinking of the TIME VALUE of an option, meaning if it had time left there was a POSITIVE time value. In the case of theta it is almost always negative. That is because theta is a measure of the passage of time (not the amount of time left). So if you look from T=0 and then go forward, theta being negative makes sense to me. Said another way. As more and more time passes you option is going to lose value (holding other inputs constant).
it’s basically option value = true value + time value time value keeps dereasing as we get closer to the expiration date, since investors are probably having the sense of the outcome of the option so close to maturity.
I was thinking as t0 was the time it expires and you were going backwards. My bad. I’m retarded.
Black Swan Wrote: ------------------------------------------------------- > He means time zero as in T(0)=====>T(1), not the > other way around, which I think is the way you’re > picturing it. LOL. Swan did a much better job of explaining it than I did…with about 1/100 of the words.
My work here is done.
Nib T=0 is equal to now. Remember this for the exam. 
Sometimes I need pre-school teaching methods and this probably means I need to give it up for the night.