Options: Calculating the 1 Sigma Expected Range for SPX

O

ondafringe

Using the numbers at Friday's close... for the contract that expires this Monday, 10/17:

ATM Straddle Method

Using the p/c premium mid-price for the 3585 strike:

((55.50 * 0.84) / 3585) * 3585 = +/- 46.62

ER (from the 3585 strike) = 3538.38 to 3631.62


IV Method

Using the p/c average IV for the 3585 strike:

(3585 * (26.43 / 100)) * (√(1/365)) = +/- 49.60

ER (from the 3585 strike) = 3535.40 to 3634.60


I'm not sure whether the above calculations should be equal or just reasonably close, or maybe I made a mistake.

However, from what I understand, the above expected range calculations for SPX should equal 1 sigma... and 1 sigma should equal a 16 delta... but it doesn't. A 16 delta call is around 3653 and a 16 delta put is around 3510, giving an ER = 3510 to 3653. Not even close to the above calculations.

Where have I gone wrong and/or what am I not understanding?
 
IMHO: It really depends on what "YOU" are looking for! Most seem very sloppy in vague references to what they want, and then muddy the water more by using crapily constructed metrics. So, expect if you can drill into specifically what it is you are seeking, you can arrive at an appropriate reliable method of representing it.
While not for everyone, I prefer using the ATM IV of the nearest timeframe I am interested in, then compute using precise formula (up/down is not symmetrical in distance). Even if you do the best possible, you remain subject to differences between expectations (actual prices) and what "will" occur, which may differ from expectations.
 
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The expected value (under a lognormal distribution and for smaller IV/time to expiry) of an ATM straddle is about .8*Spot*IV*sqrt(years to exp). Grouping IV*sqrt(years to exp) together as the standard deviation, we see that the fair value of a straddle is about 80% of one standard deviation as opposed to 100% of one standard deviation.
 
Just noticed you are referencing Monday's expiration! You are also hampered by proper handling of non-trading days which seems to be a sticky wicket! -- I retracted my earlier post of ATM IV which was for different expiration. Monday's expiration data from Friday's close has excessive error content for me to provide useful data (so I don't bother).
 
stepandfetchit said:
Just noticed you are referencing Monday's expiration! You are also hampered by proper handling of non-trading days which seems to be a sticky wicket! -- I retracted my earlier post of ATM IV which was for different expiration. Monday's expiration data from Friday's close has excessive error content for me to provide useful data (so I don't bother).
More...
If you use the same number of days the software which gives you an IV, both trading days and IV will be wrong but their product IV*sqrt(time) should be right.
 
stepandfetchit said:
Just noticed you are referencing Monday's expiration! You are also hampered by proper handling of non-trading days which seems to be a sticky wicket! -- I retracted my earlier post of ATM IV which was for different expiration. Monday's expiration data from Friday's close has excessive error content for me to provide useful data (so I don't bother).
More...

Yes, my interest is in SPX 0DTE. I used 1DTE for my calculations (from tomorrow's (Sunday's) Globex open). Using delta may be easier, but I would really like to understand the calculation part. Thanks for your input, though.
 
tooriginal said:
The expected value (under a lognormal distribution and for smaller IV/time to expiry) of an ATM straddle is about .8*Spot*IV*sqrt(years to exp). Grouping IV*sqrt(years to exp) together as the standard deviation, we see that the fair value of a straddle is about 80% of one standard deviation as opposed to 100% of one standard deviation.
More...

That's interesting. Can you provide a link where I can do some reading on this? Since my interest is in SPX 0DTE, I'm wondering if there is a *reasonably* reliable way to calculate ER at various points throughout the day of expiration... or whether the closer you get to expiration (the close of that day), the less reliable ER becomes.
 
Using DTE=2 IV=26.43 Spot=3585 :
Code: 
S=3585.000000 IV=26.430000 DTE=2.000000(t=0.005479) rPct=0.000000 qPct=0.000000 z=+1.000000 --> Sx=3655.8329
S=3585.000000 IV=26.430000 DTE=2.000000(t=0.005479) rPct=0.000000 qPct=0.000000 z=-1.000000 --> Sx=3515.5434
.

Using DTE=3 IV=26.43 Spot=3585 :
Code: 
S=3585.000000 IV=26.430000 DTE=3.000000(t=0.008219) rPct=0.000000 qPct=0.000000 z=+1.000000 --> Sx=3671.9389
S=3585.000000 IV=26.430000 DTE=3.000000(t=0.008219) rPct=0.000000 qPct=0.000000 z=-1.000000 --> Sx=3500.1195
 
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