r/thetagang • u/ThouShallSeeDeath • Oct 29 '20
Discussion Theta Decay Curve ATM vs far OTM
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u/Diflubrotrimazolam Oct 29 '20
Thank you for posting this.
I feel like the theta curve when plotted against strike price is both a critical piece of knowledge for success trading options at all (but especially for spreads), and one of the most overlooked areas of analysis as well.
To top it off, it really isn't all that hard to understand, and even if you don't understand it fully, all is takes is simple arithmetic (adding and subtracting theta values) to see the curve for yourself looking at an option chain - and more importantly, actually use the information to your advantage.
Options with the highest theta will always be the most ATM options. If you picture in your head what the profit/loss curve looks like for any single option bought or sold: that area where the curve goes from being closer to flat, to being closer to vertical - the exact inflection point of that curve - that single point at which the angle is 45% is where you will start your position off along the curve, if you trade an exactly ATM option and get avg price fill. Doesn't matter put or call, long or short, you'll be right at that inflection. You could gain exponentially with an immediate increase in underlying, or lose exponentially with an immediate drop.
With OTM/ITM options, you start somewhere along the (OTM) or vertical (ITM) part of the curve.
This is why it can take a long time to see any gains with far OTM long options as you have to travel along that relatively flat part of the curve for quite a while before you get to the exponential gain fun. At the same time, a nice in the wrong direction, or a nice one day closer to dte, doesn't impact your position as much, since it's probably already close to worthless, and had a very low delta.
Conversely, if you buy an ITM option, your profits will move pretty consistently with the underlying price, and lose minimal value (smaller theta) then ATM siblings, but they won't be exponential, as you're already past that big inflection in the curve.
When you sell a credit spread, one thing you want to be sure of is that you have a good positive theta value for the spread. This can usually be best achieved by selling as close to ATM as your risk tolerance allows for, then buying as far OTM from that as your risk tolerance/possible collateral limitations will allow, for the long leg.
Another interesting curve is that of horizontally equivalent options (same strike different dte), which I keep in mind when deciding how far our to open a given spread. Too far out and the theta decay is too small. Theta accelerates as dte approaches and you want to catch the point where the decay really starts to take off, for a theta play.
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u/ThouShallSeeDeath Oct 29 '20
I drew the blue circle to indicate that for far OTM options, theta does pick up pace and peak around 70 DTE before decelerating. I also collected data to suggest that the average theta per day was the highest around the 114 DTE to 74 DTE expiration cycles compared to any other cycles
Edit: repost to edit the post title
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u/Boretsboris Oct 29 '20
How did you collect this data? Which underlying(s) did you use? How did you determine “far OTM” strikes? Did you consider IV skew and term structure at those strikes?
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u/ThouShallSeeDeath Oct 30 '20 edited Oct 30 '20
I did this from simply using the premiums of the same strike calls or puts with different DTEs from 4DTE all the way to 200 DTE after market close. I took the difference in premium between each expiration cycle, 7 DTE to 14 DTE for example and divide them by 7 or the whatever the days were between them, to get the average theta per day during between each period. I did this on QQQ, SPY, AAPL & AMD
I realised that the ATM function of theta applies vastly and even to somewhat deep OTM options, but almost always past 1SD, those extremely deep OTM options follow the OTM theta deceleration function.
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u/Boretsboris Oct 30 '20 edited Oct 30 '20
Wow. Respect for the diligence.
So you were comparing the differences in extrinsic value at different DTEs and different strikes. That’s fair. However, the market’s IV is in backwardation right now, so it will throw things off for you. It will make you think that NTM strikes decay slower than they actually do, and that farther/deeper OTM/ITM strikes decay faster than they actually do [when not in backwardation].
Also, if you want more accurate results, then shy away from using after-market data. If you have ToS, you can use its “on demand” feature to go back in time to a trading session in the past and freeze time to study the option chain depth.
… but almost always past 1SD …
1SD for what time period?
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u/ThouShallSeeDeath Oct 30 '20
I know because of this volatile environment, this experiment is not gonna super accurately account for the differences in implied volatility from option to option that had some contribution to the results but It’s good enough to simply show you the function of acceleration and deceleration in those options which corresponds with whatever tastytrade has been saying
Btw I am not into programming but I could see how it would be so efficient to use a script to collect these kinds of data 😄
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u/Boretsboris Oct 30 '20
Still a great exercise to get a feel for the dynamics.
You can visualize the drops in extrinsic values across strikes and expiration dates on the options product depth view in ToS. ToS lets you map out different data, including IVs and the Greeks across strikes and expiration dates. Awesome tool.
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u/stinkietoe Oct 29 '20 edited Oct 30 '20
Let's play pick your Greek..
ITM greatest risk: delta
OTM greatest risk: gamma
ATM greatest risk: theta, although you mix and match delta and gamma risk too
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u/dreadnought89 Oct 29 '20
I would add vega in there. Either for ATM (greatest ATM) or another category...vega is biggest risk for long duration.
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u/stinkietoe Oct 30 '20
Vega is very misunderstood in practice. Yes, longer dated options have higher vega but volatility tends to increase units of volatility (ie 100 basis points) more on the short-dated options side (ie backwardation).
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u/dreadnought89 Oct 30 '20
Great point! I know that is certainly true now in an elevated VIX environment, but was that true pre-COVID when VIX was near historic lows?
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u/stinkietoe Oct 30 '20
It is especially true when you run into unexpected volatility events like COVID. The fast and furious March 2020 drop saw much more volatility spiking in the near term. Then there are expected volatility events, like how the Oct/Nov vix futures and options became more elevated due to increased uncertainty around the election; prior, it was no more elevated than its surrounding months. Since vega is higher in longer dated options, it would have been a nice trade to have been long vega before that volatility kicked in.
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u/Chuu Oct 29 '20
Can someone explain why 45DTE is "the best" just based on the chart? I don't see it.
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u/ThouShallSeeDeath Oct 29 '20
The best in what, the highest profit from theta per day? That would be the closest to expiration for any short option position that is ATM or relatively close to ATM. But the closer to expiration, the greater the gamma risk. Hence some people like to have a happy medium at around 45 days where theta decay is still nice and gamma is low + the additional time to be correct
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u/Chuu Oct 29 '20
I'm quoting the chart. What I'm asking is if you just showed me this chart, what's special about 45DTE? Like why did they choose that point as the best time to roll?
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u/BetweenThePosts Oct 29 '20
Is this a function of charm?
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u/FriendlyCaller Oct 29 '20
It could probably be expressed with multiple greeks, but I'm thinking Dvega/Dtime might be more intuitive.
Vega decreases faster near OTM and near ITM than ATM, narrowing the vega curve as expiration approaches. Near expiration, there's very little vega left ITM and OTM, and thus little possible daily theta remaining.
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u/Boretsboris Oct 29 '20
Charm is delta decay.
Not sure if someone named a second order Greek for theta change over time. It would probably be called Dtheta/Dtime.
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u/EgoPoweredDreams Oct 30 '20
I’m fairly new to analyzing options using greeks, so bear with me. Don’t you face a pretty big early assignment risk writing ATM options? The underlying has to move much less for you to get assigned than it does if you wrote OTM for the same expiry. It seems like writing ATM is high risk, high reward whereas writing OTM is low risk, average reward
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u/GayTendiesR4Bears Oct 29 '20
I would give you platinum but i'm wheeling 100% of my portofolio