The magnitude of theta rises exponentially as expiration approaches (exponential time decay) --- ONLY and ONLY --- for ATM options. Theta is more or less flat and decreases to nearly zero prior to expiration rather than increases exponentially. If an option is ATM now, it likely will not be one minute later, and much less likely to remain ATM one month later. Therefore, if you short options, you will have some time decay, but will not have the benefit of EXPONENTIAL time decay on your side (you don't have the benefit of the most powerful weapon; you only have a toy BB gun against your opponent). CBOE, OIC, and many others have taught investors exponential time decay, but I think it is misleading. Any comments?
I write options, and have learned quite a few hard lessons. Theta DOES INCREASE the closer you get to expiration, if the option is ATM or close to the money. Obviously, if the option's only worth a nickel or less, there's going to be no theta since it's practically worthless already. Or if the option is deep ITM, it's all intristic value and no time value. Theta can only erode time value, not intristic (obviously). Never hang around for the last nickel, it can easily turn into a thousand dollar loss (actually, in my case, $2500 on 10 contracts.. when I could've paid $50 + commission to close it out). I mean, unless the company's getting bought out and you sold put options, and now the stock is 20% out of the money, I can't think of any other scenario where you should be hanging around for that last nickel, there's no theta, and you're short delta and gamma for no reason.
If an OTM option with not a lot of time to expiration at $0.20 goes from $0.20 to $0.15 and then to $0.10 over 2 days holding all other factors constant, is that exponential decay or linear decay? Day 1: .20 to .15 is a decrease of - 25% Day 2: .15 to .10 is a decrease of -33% If on the next day it drops to $0.05 it is a decrease of -50% seems exponential to me. Even though I made up these numbers this kind of decay is common in OTM options.
optioncoach, depends on how you look at it. If you're looking at it purely from a theta standpoint, then it's linear if it's dropping 5 cents a day, because the 1 day theta (per share) would be 0.05, or -0.05, depending on which side you're on. Another interesting thing is that VIX options may actually have negative theta, so may other european options that have no tangible underlying.
Uhhhh.... no, it's not how you look at it. Linear decay must be met by an increase in volty. All greeks have curvature[convexity]. Coach offered an excellent analogy there.
Props to Option coach. The time decay is present and clearly visible to those who pay attention. Akuma
Time decay clearly isn't linear, ATM or not. If an option (this is theoretical) were to deteriorate at $.05 per day for 40 days, starting at $2.00, would you consider this linear? If so, you would be wrong. An option buyer would be much more severly hurt (percentage-wise) each day as expiration approached. The math should be clear. (This is simply an extension of optionscoach's assessment...)
Gamma also exponentially increase if and ONLY if the option is ATM. So, if you short an option and it moved OTM, gamma exposure is limited as expiration approaches. Being OTM also helps even if time decay is not as favorable. Being ITM is the problem.
Regardless of ATM or OTM, time decay is not linear, itâs exponential. The difference between ATM and OTM decay only becomes apparent in the last few days of option life. ATM has the most time value, so the decay will be rapid as expiry approaches, and will look like a fat tail if you graph it. OTM has very little time value to lose now, and so the decay is less rapid and will look like a flat tail if you graph it. I don't think there's anything "mythical" about this.