I am relatively new to options trading and have one question regarding theta: SPY is closed at $249.19 today. In thinkorswim, in October expiry, ATM strike 249P shows a theta of 0.03, smaller than 0.04 theta of OTM strike 245P, in terms of absolute value. Is this reasonable? I thought the ATM strike should decay faster than OTM strike... Does this mean that if I make this bullish OTM vertical +245P/-249P, I will be suffering theta decay with passage of time (assuming IV and underlying price do not change)?
Similarly, among UVXY OTM calls, the peak of theta is not at the ATM strike 25; the peak -0.047 resides on 32-42 (around 1 standard deviation strike). If I place this bearish OTM call vertical -25C/+35C, will I be suffering theta decay with passage of time (assuming IV and underlying price do not change)?
I would not assume the difference between 0.03 and 0.04 is material and the underlying will move. I can tell you at if the SPY is at one strike with one to two days left, that option will have a much higher value than one that is 4 points away. So, the one 4 points way has a faster track to $0.00. I would focus more on what your expectation are for the SPY from now until October and the best way to monetize that, rather than focusing on the greeks. The greeks are a tool for managing risk, not finding profitable trades.
http://www.schwab.com/public/file?cmsid=Time-Value-Erosion&filename=Time_Value_Erosion&cv1 OTM options' decay is nearly linear; ATM is more like a thrown wad of paper across the room. Note also, that OTM decay stalls dramatically in the last week/day/hours -- and you'll see a concomitant increase in IV on those as well. (Just to solve that mystery when you see it.)
to add more confusion, throw in the skew and the absolute levels of IV which could make the theta difference between the strikes even closer. IOW if IV is crazy high, every strike is ATM.. sorta...
I think that is usually true if you mean "faster" as a percentage of the price of the option rather than the price of the underlying, but not if you mean for a given amount of underlying. The premium of all options goes to zero at expiration, and, unless we're dealing with very high volatilities and long lived options, the maximum premium for any given series of options with the same expiration and underlying should be at a strike close to the price of the underlying ("at the money"). So, consider the case where the underlying remains at the same price until expiration, if an at the money option starts with more premium than an out of the money option, and both go to zero, there must be some point at which their difference decreases. When that occurs, the theta of the option with higher premium (the at the money option) must be more negative than the theta of the out of the money option. I would have a more difficult time proving the following, but I think that the theta of an option with higher premium should always be more negative than the theta of a lower premium option with the same underlying and expiration. The reason I have such a problem believing that is if I consider a spread made by going long the high premium option and short the low premium option, the proposition that the low premium option could have a more negative theta would mean that this spread, which would have zero value at expiration if the underlying ends up then being at its current value, would somehow gain in value if the underlying does not move and the expiration time is shortened.
This graph looks wrong to me because, if I were to draw more lines of "in the money" and "out of the money" options by adding lines for strikes gradually getting closer to the money, I would expect "at the money" to be some sort of convergence between "in the money" and "out of the money", which is not the case in this graph. Also, to the extent that put-call parity applies, every out of the money option of one type (get or put) should have a corresponding in-the-money option that is the same except that the type is reversed (put or get, respectively) with approximately the same premium, and likewise for in the money options having a corresponding out of the money option of opposite type with approximately the same premium. So, I think that graph is mislabeled. For starters, the currently unlabeled vertical access should be labeled "premium." More substantially, the green "In the money" line should be relabeled "near (both in and out of the money)", and the blue "out of the money" line should be relabeled "far (both in and out of the money)." This is much more consistent, as "near" should be some average between "at" and "far", and the premium of "far" should get closer to horizontal earlier just because its premiums will become nearly zero much earlier and then just can't drop below zero. A web search for '"Time Value Erosion" Schwab' found this document, which contains that diagram: http://www.schwab.com/public/schwab.../options/how_to_understand_option_greeks.html , and that document introduces that diagram with a couple of notes, one of which refers to the comparison as being with "far out of the money" options, even though it is not labeled as such in the graph.
1. OTM options are 100% time value premium so the decay is greater as a % of the option's price but how fast is the decay depends on time to expiration, you cannot just look at the value of theta. If these are 90 day options the decay is minimal versus September expiry. When we say decay is greater or lesser we have to look beyond the actual theta value and see it as a % of the option price. In other words a theta of -.05 on an ATM option @ $3.50 or a theta of -.03 on OTM options @ $0.20. Which has greater decay? 2. ALL verticals suffer theta decay with passage of time holding IV and underlying constant. That is what theta is.
That is if we assume Black-Scholes is completely correct (IV across all strikes and all expirations are the same) which we know it's not (skew). In this case the ATM strike for Puts has around a 6% IV and the OTM 245 put has an IV of 9%. The closed-form formula for theta has IV on the numerator (among other terms) so that is what might be throwing the numbers off. Keep in mind that the greeks are only approximations and not too much should be read into their exact value Yes, for a certain skew and depending on moneyness (where the underlying is in relation to the strikes) you could have a Credit Put Spread with negative theta... or conversely a Debit Put Spread (bearish) with positive theta. I actually take advantage of this quite often where I will buy a put spread with the underlying in the middle (50/50) where I am buying it for less than its time value (so I am theta positive) even though it's a 50/50 shot. For example, if you buy the 250/245 Put Spread with the underlying at 247.50 you'd expect it to be worth 2.50 but because of skew sometimes you can buy it for, say 2.10. This is all because of skew, which is more pronounced in Indices and Index-tracking products.